Theorem 3cubeslem3l

Description: Lemma for 3cubes . (Contributed by Igor Ieskov, 22-Jan-2024)

	Ref	Expression
Hypothesis	3cubeslem1.a	$$⊢\phi \to A\in \mathbb{Q}$$
Assertion	3cubeslem3l	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A^7{3}^9+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		3cubeslem1.a	$$⊢\phi \to A\in \mathbb{Q}$$
2		3cn	$$⊢3\in ℂ$$
3	2	a1i	$$⊢\phi \to 3\in ℂ$$
4		3nn0	$$⊢3\in {\mathbb{N}}_0$$
5	4	a1i	$$⊢\phi \to 3\in {\mathbb{N}}_0$$
6	3 5	expcld	$$⊢\phi \to 3^3\in ℂ$$
7		qcn	$$⊢A\in \mathbb{Q}\to A\in ℂ$$
8	1 7	syl	$$⊢\phi \to A\in ℂ$$
9	8	sqcld	$$⊢\phi \to A^2\in ℂ$$
10	6 9	mulcld	$$⊢\phi \to 3^3{A}^2\in ℂ$$
11	3	sqcld	$$⊢\phi \to 3^2\in ℂ$$
12	11 8	mulcld	$$⊢\phi \to 3^{2}A\in ℂ$$
13	10 12 3	cu3addd	$$⊢\phi \to {\left(3^3{A}^2+3^{2}A+3\right)}^3=\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3$$
14	13	oveq2d	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)$$
15	10 5	expcld	$$⊢\phi \to {3^3{A}^2}^3\in ℂ$$
16	10	sqcld	$$⊢\phi \to {3^3{A}^2}^2\in ℂ$$
17	16 12	mulcld	$$⊢\phi \to {3^3{A}^2}^2{3}^{2}A\in ℂ$$
18	3 17	mulcld	$$⊢\phi \to 3{3^3{A}^2}^2{3}^{2}A\in ℂ$$
19	15 18	addcld	$$⊢\phi \to {3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\in ℂ$$
20	12	sqcld	$$⊢\phi \to {3^{2}A}^2\in ℂ$$
21	10 20	mulcld	$$⊢\phi \to 3^3{A}^2{3^{2}A}^2\in ℂ$$
22	3 21	mulcld	$$⊢\phi \to 33^3{A}^2{3^{2}A}^2\in ℂ$$
23	12 5	expcld	$$⊢\phi \to {3^{2}A}^3\in ℂ$$
24	22 23	addcld	$$⊢\phi \to 33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\in ℂ$$
25	19 24	addcld	$$⊢\phi \to {3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\in ℂ$$
26	16 3	mulcld	$$⊢\phi \to {3^3{A}^2}^2\cdot 3\in ℂ$$
27	3 26	mulcld	$$⊢\phi \to 3{3^3{A}^2}^2\cdot 3\in ℂ$$
28		2nn0	$$⊢2\in {\mathbb{N}}_0$$
29	28	a1i	$$⊢\phi \to 2\in {\mathbb{N}}_0$$
30	5 29	nn0mulcld	$$⊢\phi \to 3\cdot 2\in {\mathbb{N}}_0$$
31	30	nn0cnd	$$⊢\phi \to 3\cdot 2\in ℂ$$
32	10 12	mulcld	$$⊢\phi \to 3^3{A}^2{3}^{2}A\in ℂ$$
33	31 32	mulcld	$$⊢\phi \to 3\cdot 23^3{A}^2{3}^{2}A\in ℂ$$
34	33 3	mulcld	$$⊢\phi \to 3\cdot 23^3{A}^2{3}^{2}A\cdot 3\in ℂ$$
35	27 34	addcld	$$⊢\phi \to 3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\in ℂ$$
36	20 3	mulcld	$$⊢\phi \to {3^{2}A}^2\cdot 3\in ℂ$$
37	3 36	mulcld	$$⊢\phi \to 3{3^{2}A}^2\cdot 3\in ℂ$$
38	35 37	addcld	$$⊢\phi \to 3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\in ℂ$$
39	25 38	addcld	$$⊢\phi \to \left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+3{3^{2}A}^2\cdot 3\in ℂ$$
40	10 11	mulcld	$$⊢\phi \to 3^3{A}^2{3}^2\in ℂ$$
41	3 40	mulcld	$$⊢\phi \to 33^3{A}^2{3}^2\in ℂ$$
42	12 11	mulcld	$$⊢\phi \to 3^{2}A{3}^2\in ℂ$$
43	3 42	mulcld	$$⊢\phi \to 33^{2}A{3}^2\in ℂ$$
44	41 43	addcld	$$⊢\phi \to 33^3{A}^2{3}^2+33^{2}A{3}^2\in ℂ$$
45	44 6	addcld	$$⊢\phi \to 33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\in ℂ$$
46	8 39 45	adddid	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
47	8 25 38	adddid	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+3{3^{2}A}^2\cdot 3\right)=A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)$$
48	47	oveq1d	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
49	46 48	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
50	8 19 24	adddid	$$⊢\phi \to A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)=A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)$$
51	50	oveq1d	$$⊢\phi \to A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)=A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)$$
52	51	oveq1d	$$⊢\phi \to A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=\left(A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
53	49 52	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=\left(A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
54	8 15 18	adddid	$$⊢\phi \to A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A$$
55	54	oveq1d	$$⊢\phi \to A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)$$
56	55	oveq1d	$$⊢\phi \to A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)$$
57	56	oveq1d	$$⊢\phi \to \left(A\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
58	53 57	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
59	8 22 23	adddid	$$⊢\phi \to A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)=A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3$$
60	59	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3$$
61	60	oveq1d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)$$
62	61	oveq1d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A\left(33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
63	58 62	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
64	8 35 37	adddid	$$⊢\phi \to A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)=A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3$$
65	64	oveq2d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3$$
66	65	oveq1d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
67	63 66	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
68	8 27 34	adddid	$$⊢\phi \to A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3$$
69	68	oveq1d	$$⊢\phi \to A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3$$
70	69	oveq2d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3$$
71	70	oveq1d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
72	67 71	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)$$
73	8 44 6	adddid	$$⊢\phi \to A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=A\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+A{3}^3$$
74	73	oveq2d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+A{3}^3$$
75	72 74	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+A{3}^3$$
76	8 41 43	adddid	$$⊢\phi \to A\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)=A33^3{A}^2{3}^2+A33^{2}A{3}^2$$
77	76	oveq1d	$$⊢\phi \to A\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+A{3}^3=A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3$$
78	77	oveq2d	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+A\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+A{3}^3=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3$$
79	75 78	eqtrd	$$⊢\phi \to A\left(\left({3^3{A}^2}^3+3{3^3{A}^2}^2{3}^{2}A+33^3{A}^2{3^{2}A}^2+{3^{2}A}^3\right)+\left(3{3^3{A}^2}^2\cdot 3+3\cdot 23^3{A}^2{3}^{2}A\cdot 3+3{3^{2}A}^2\cdot 3\right)+\left(33^3{A}^2{3}^2+33^{2}A{3}^2\right)+3^3\right)=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3$$
80	14 79	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3$$
81	8 15	mulcld	$$⊢\phi \to A{3^3{A}^2}^3\in ℂ$$
82	8 18	mulcld	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A\in ℂ$$
83	81 82	addcld	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\in ℂ$$
84	8 22	mulcld	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2\in ℂ$$
85	8 23	mulcld	$$⊢\phi \to A{3^{2}A}^3\in ℂ$$
86	84 85	addcld	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\in ℂ$$
87	83 86	addcld	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\in ℂ$$
88	8 27	mulcld	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3\in ℂ$$
89	8 34	mulcld	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\in ℂ$$
90	88 89	addcld	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\in ℂ$$
91	8 37	mulcld	$$⊢\phi \to A3{3^{2}A}^2\cdot 3\in ℂ$$
92	90 91	addcld	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\in ℂ$$
93	8 41	mulcld	$$⊢\phi \to A33^3{A}^2{3}^2\in ℂ$$
94	8 43	mulcld	$$⊢\phi \to A33^{2}A{3}^2\in ℂ$$
95	93 94	addcld	$$⊢\phi \to A33^3{A}^2{3}^2+A33^{2}A{3}^2\in ℂ$$
96	8 6	mulcld	$$⊢\phi \to A{3}^3\in ℂ$$
97	95 96	addcld	$$⊢\phi \to A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\in ℂ$$
98	87 92 97	addassd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=\left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)$$
99	92 97	addcld	$$⊢\phi \to \left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\in ℂ$$
100	83 86 99	addassd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A\right)+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)$$
101	98 100	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)$$
102	86 99	addcld	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)\in ℂ$$
103	81 82 102	addassd	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)\right)$$
104	101 103	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)\right)$$
105	84 85 99	addassd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)=A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)$$
106	105	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)\right)$$
107	106	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)\right)$$
108	104 107	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)\right)$$
109	85 99	addcomd	$$⊢\phi \to A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)=\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3$$
110	109	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)=A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A{3^{2}A}^3$$
111	110	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A{3^{2}A}^3+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)$$
112	111	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A{3^{2}A}^3\right)$$
113	108 112	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A{3^{2}A}^3\right)$$
114	92 97 85	addassd	$$⊢\phi \to \left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3=\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3$$
115	114	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A{3^{2}A}^3=A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)$$
116	115	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)$$
117	116	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A{3^{2}A}^3\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)$$
118	113 117	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)$$
119	97 85	addcld	$$⊢\phi \to \left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\in ℂ$$
120	90 91 119	addassd	$$⊢\phi \to \left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)$$
121	120	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)=A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)$$
122	121	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)$$
123	122	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)\right)$$
124	118 123	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)\right)$$
125	91 119	addcld	$$⊢\phi \to A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\in ℂ$$
126	88 89 125	addassd	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)$$
127	126	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)$$
128	127	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)\right)$$
129	128	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3\right)+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)\right)$$
130	124 129	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)\right)$$
131	91 119	addcomd	$$⊢\phi \to A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3=\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3+A3{3^{2}A}^2\cdot 3$$
132	131	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)+A3{3^{2}A}^2\cdot 3$$
133	132	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3+A3{3^{2}A}^2\cdot 3\right)$$
134	133	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)+A3{3^{2}A}^2\cdot 3\right)$$
135	134	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A3{3^{2}A}^2\cdot 3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3+A3{3^{2}A}^2\cdot 3\right)\right)$$
136	135	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)$$
137	130 136	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)$$
138	97 85	addcomd	$$⊢\phi \to \left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3=A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3$$
139	138	oveq1d	$$⊢\phi \to \left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3+A3{3^{2}A}^2\cdot 3=A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3$$
140	139	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)+A3{3^{2}A}^2\cdot 3=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A3{3^{2}A}^2\cdot 3$$
141	140	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3+A3{3^{2}A}^2\cdot 3\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)$$
142	141	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)+A3{3^{2}A}^2\cdot 3\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)$$
143	142	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A{3^{2}A}^3+A3{3^{2}A}^2\cdot 3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)$$
144	143	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A{3^{2}A}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)$$
145	137 144	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)$$
146	85 97 91	addassd	$$⊢\phi \to A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3=A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3$$
147	146	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A3{3^{2}A}^2\cdot 3=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3\right)$$
148	147	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)$$
149	148	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)$$
150	149	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)$$
151	150	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)$$
152	145 151	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)$$
153	95 96 91	addassd	$$⊢\phi \to \left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3=A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3$$
154	153	oveq2d	$$⊢\phi \to A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3=A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)$$
155	154	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)$$
156	155	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)$$
157	156	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)$$
158	157	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3\right)+A3{3^{2}A}^2\cdot 3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)$$
159	158	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)$$
160	152 159	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)$$
161	96 91	addcld	$$⊢\phi \to A{3}^3+A3{3^{2}A}^2\cdot 3\in ℂ$$
162	93 94 161	addassd	$$⊢\phi \to A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3=A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)$$
163	162	oveq2d	$$⊢\phi \to A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)=A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)$$
164	163	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)$$
165	164	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)$$
166	165	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)$$
167	166	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)$$
168	167	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)\right)$$
169	160 168	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)\right)$$
170	94 161	addcomd	$$⊢\phi \to A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3=A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2$$
171	170	oveq2d	$$⊢\phi \to A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)=A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2$$
172	171	oveq2d	$$⊢\phi \to A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)=A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2\right)$$
173	172	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2\right)$$
174	173	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2\right)\right)$$
175	174	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2\right)\right)$$
176	175	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A33^{2}A{3}^2+A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2\right)\right)\right)$$
177	176	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2\right)\right)\right)$$
178	169 177	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2\right)\right)\right)$$
179	96 91	addcomd	$$⊢\phi \to A{3}^3+A3{3^{2}A}^2\cdot 3=A3{3^{2}A}^2\cdot 3+A{3}^3$$
180	179	oveq1d	$$⊢\phi \to A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2=A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2$$
181	180	oveq2d	$$⊢\phi \to A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2=A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2$$
182	181	oveq2d	$$⊢\phi \to A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2\right)=A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)$$
183	182	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2\right)$$
184	183	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2\right)\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)$$
185	184	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2\right)\right)$$
186	185	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2\right)\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)\right)$$
187	186	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A{3}^3+A3{3^{2}A}^2\cdot 3\right)+A33^{2}A{3}^2\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2\right)\right)\right)$$
188	178 187	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2\right)\right)\right)$$
189	91 96 94	addassd	$$⊢\phi \to A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2=A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2$$
190	189	oveq2d	$$⊢\phi \to A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2=A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)$$
191	190	oveq2d	$$⊢\phi \to A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)=A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)$$
192	191	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)\right)$$
193	192	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)$$
194	193	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)\right)\right)$$
195	194	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)\right)$$
196	195	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3\right)+A33^{2}A{3}^2\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)\right)\right)\right)$$
197	188 196	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)\right)\right)\right)$$
198	96 94	addcomd	$$⊢\phi \to A{3}^3+A33^{2}A{3}^2=A33^{2}A{3}^2+A{3}^3$$
199	198	oveq2d	$$⊢\phi \to A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2=A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3$$
200	199	oveq2d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)=A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)$$
201	200	oveq2d	$$⊢\phi \to A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)=A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)$$
202	201	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)$$
203	202	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)=A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)$$
204	203	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
205	204	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A{3}^3+A33^{2}A{3}^2\right)\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
206	205	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A{3}^3+A33^{2}A{3}^2\right)\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)\right)$$
207	197 206	eqtrd	$$⊢\phi \to \left(A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+A{3^{2}A}^3\right)+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A3{3^{2}A}^2\cdot 3\right)+\left(A33^3{A}^2{3}^2+A33^{2}A{3}^2\right)+A{3}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)\right)$$
208	80 207	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)\right)$$
209	94 96	addcld	$$⊢\phi \to A33^{2}A{3}^2+A{3}^3\in ℂ$$
210	91 209	addcld	$$⊢\phi \to A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\in ℂ$$
211	93 210	addcld	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\in ℂ$$
212	85 211	addcld	$$⊢\phi \to A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\in ℂ$$
213	89 212	addcld	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\in ℂ$$
214	84 88 213	addassd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
215	214	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A33^3{A}^2{3^{2}A}^2+\left(A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
216	215	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)\right)$$
217	216	eqcomd	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
218	89 85 211	addassd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)$$
219	218	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)$$
220	219	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
221	220	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+\left(A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
222	217 221	eqtr4d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
223	93 91 209	addassd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3=A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)$$
224	223	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A33^{2}A{3}^2+A{3}^3\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)$$
225	224	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)$$
226	225	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A33^{2}A{3}^2+A{3}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A33^3{A}^2{3}^2+\left(A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)$$
227	226	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)$$
228	222 227	eqtr4d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+\left(A33^{2}A{3}^2+A{3}^3\right)\right)\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)$$
229	208 228	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)$$
230	3 42	mulcomd	$$⊢\phi \to 33^{2}A{3}^2=3^{2}A{3}^2\cdot 3$$
231	230	oveq2d	$$⊢\phi \to A33^{2}A{3}^2=A{3}^{2}A{3}^2\cdot 3$$
232	11 8	mulcomd	$$⊢\phi \to 3^{2}A=A{3}^2$$
233	232	oveq1d	$$⊢\phi \to 3^{2}A{3}^2=A{3}^2{3}^2$$
234	233	oveq1d	$$⊢\phi \to 3^{2}A{3}^2\cdot 3=A{3}^2{3}^2\cdot 3$$
235	234	oveq2d	$$⊢\phi \to A{3}^{2}A{3}^2\cdot 3=AA{3}^2{3}^2\cdot 3$$
236	231 235	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=AA{3}^2{3}^2\cdot 3$$
237	8 11	mulcld	$$⊢\phi \to A{3}^2\in ℂ$$
238	237 11 3	mulassd	$$⊢\phi \to A{3}^2{3}^2\cdot 3=A{3}^2{3}^2\cdot 3$$
239	238	oveq2d	$$⊢\phi \to AA{3}^2{3}^2\cdot 3=AA{3}^2{3}^2\cdot 3$$
240	236 239	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=AA{3}^2{3}^2\cdot 3$$
241	11 3	mulcld	$$⊢\phi \to 3^2\cdot 3\in ℂ$$
242	8 11 241	mulassd	$$⊢\phi \to A{3}^2{3}^2\cdot 3=A{3}^2{3}^2\cdot 3$$
243	242	oveq2d	$$⊢\phi \to AA{3}^2{3}^2\cdot 3=AA{3}^2{3}^2\cdot 3$$
244	240 243	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=AA{3}^2{3}^2\cdot 3$$
245	11 241	mulcld	$$⊢\phi \to 3^2{3}^2\cdot 3\in ℂ$$
246	8 8 245	mulassd	$$⊢\phi \to AA{3}^2{3}^2\cdot 3=AA{3}^2{3}^2\cdot 3$$
247	246	eqcomd	$$⊢\phi \to AA{3}^2{3}^2\cdot 3=AA{3}^2{3}^2\cdot 3$$
248	11 11 3	mulassd	$$⊢\phi \to 3^2{3}^2\cdot 3=3^2{3}^2\cdot 3$$
249	248	oveq2d	$$⊢\phi \to AA{3}^2{3}^2\cdot 3=AA{3}^2{3}^2\cdot 3$$
250	247 249	eqtr4d	$$⊢\phi \to AA{3}^2{3}^2\cdot 3=AA{3}^2{3}^2\cdot 3$$
251	244 250	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=AA{3}^2{3}^2\cdot 3$$
252	8	sqvald	$$⊢\phi \to A^2=AA$$
253	252	eqcomd	$$⊢\phi \to AA=A^2$$
254	253	oveq1d	$$⊢\phi \to AA{3}^2{3}^2\cdot 3=A^2{3}^2{3}^2\cdot 3$$
255	251 254	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=A^2{3}^2{3}^2\cdot 3$$
256	3 29 29	expaddd	$$⊢\phi \to 3^{2+2}=3^2{3}^2$$
257	256	oveq1d	$$⊢\phi \to 3^{2+2}\cdot 3=3^2{3}^2\cdot 3$$
258	257	eqcomd	$$⊢\phi \to 3^2{3}^2\cdot 3=3^{2+2}\cdot 3$$
259	29 29	nn0addcld	$$⊢\phi \to 2+2\in {\mathbb{N}}_0$$
260	3 259	expp1d	$$⊢\phi \to 3^{2+2+1}=3^{2+2}\cdot 3$$
261	258 260	eqtr4d	$$⊢\phi \to 3^2{3}^2\cdot 3=3^{2+2+1}$$
262	261	oveq2d	$$⊢\phi \to A^2{3}^2{3}^2\cdot 3=A^2{3}^{2+2+1}$$
263	255 262	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=A^2{3}^{2+2+1}$$
264		2p2e4	$$⊢2+2=4$$
265	264	a1i	$$⊢\phi \to 2+2=4$$
266	265	oveq1d	$$⊢\phi \to 2+2+1=4+1$$
267	266	oveq2d	$$⊢\phi \to 3^{2+2+1}=3^{4+1}$$
268	267	oveq2d	$$⊢\phi \to A^2{3}^{2+2+1}=A^2{3}^{4+1}$$
269	263 268	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=A^2{3}^{4+1}$$
270		4p1e5	$$⊢4+1=5$$
271	270	a1i	$$⊢\phi \to 4+1=5$$
272	271	oveq2d	$$⊢\phi \to 3^{4+1}=3^5$$
273	272	oveq2d	$$⊢\phi \to A^2{3}^{4+1}=A^2{3}^5$$
274	269 273	eqtrd	$$⊢\phi \to A33^{2}A{3}^2=A^2{3}^5$$
275	274	oveq1d	$$⊢\phi \to A33^{2}A{3}^2+A{3}^3=A^2{3}^5+A{3}^3$$
276	275	oveq2d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3=A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A^2{3}^5+A{3}^3$$
277	276	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A33^{2}A{3}^2+A{3}^3\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A^2{3}^5+A{3}^3\right)$$
278	277	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A^2{3}^5+A{3}^3\right)$$
279	278	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A33^{2}A{3}^2+A{3}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A^2{3}^5+A{3}^3\right)\right)$$
280	279	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A33^{2}A{3}^2+A{3}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A^2{3}^5+A{3}^3\right)\right)$$
281	229 280	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A^2{3}^5+A{3}^3\right)\right)$$
282	8 41	mulcomd	$$⊢\phi \to A33^3{A}^2{3}^2=33^3{A}^2{3}^{2}A$$
283	3 40	mulcomd	$$⊢\phi \to 33^3{A}^2{3}^2=3^3{A}^2{3}^2\cdot 3$$
284	283	oveq1d	$$⊢\phi \to 33^3{A}^2{3}^{2}A=3^3{A}^2{3}^2\cdot 3A$$
285	282 284	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=3^3{A}^2{3}^2\cdot 3A$$
286	6 9	mulcomd	$$⊢\phi \to 3^3{A}^2=A^2{3}^3$$
287	286	oveq1d	$$⊢\phi \to 3^3{A}^2{3}^2=A^2{3}^3{3}^2$$
288	287	oveq1d	$$⊢\phi \to 3^3{A}^2{3}^2\cdot 3=A^2{3}^3{3}^2\cdot 3$$
289	288	oveq1d	$$⊢\phi \to 3^3{A}^2{3}^2\cdot 3A=A^2{3}^3{3}^2\cdot 3A$$
290	285 289	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^2{3}^3{3}^2\cdot 3A$$
291	9 6	mulcld	$$⊢\phi \to A^2{3}^3\in ℂ$$
292	291 11	mulcld	$$⊢\phi \to A^2{3}^3{3}^2\in ℂ$$
293	292 3 8	mulassd	$$⊢\phi \to A^2{3}^3{3}^2\cdot 3A=A^2{3}^3{3}^{2}3A$$
294	290 293	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^2{3}^3{3}^{2}3A$$
295	3 8	mulcld	$$⊢\phi \to 3A\in ℂ$$
296	291 11 295	mulassd	$$⊢\phi \to A^2{3}^3{3}^{2}3A=A^2{3}^3{3}^{2}3A$$
297	294 296	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^2{3}^3{3}^{2}3A$$
298	11 295	mulcld	$$⊢\phi \to 3^{2}3A\in ℂ$$
299	9 6 298	mulassd	$$⊢\phi \to A^2{3}^3{3}^{2}3A=A^2{3}^3{3}^{2}3A$$
300	297 299	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^2{3}^3{3}^{2}3A$$
301	6 298	mulcomd	$$⊢\phi \to 3^3{3}^{2}3A=3^{2}3A{3}^3$$
302	301	oveq2d	$$⊢\phi \to A^2{3}^3{3}^{2}3A=A^2{3}^{2}3A{3}^3$$
303	300 302	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^2{3}^{2}3A{3}^3$$
304	11 295	mulcomd	$$⊢\phi \to 3^{2}3A=3A{3}^2$$
305	304	oveq1d	$$⊢\phi \to 3^{2}3A{3}^3=3A{3}^2{3}^3$$
306	305	oveq2d	$$⊢\phi \to A^2{3}^{2}3A{3}^3=A^{2}3A{3}^2{3}^3$$
307	303 306	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^{2}3A{3}^2{3}^3$$
308	3 8	mulcomd	$$⊢\phi \to 3A=A\cdot 3$$
309	308	oveq1d	$$⊢\phi \to 3A{3}^2=A\cdot 33^2$$
310	309	oveq1d	$$⊢\phi \to 3A{3}^2{3}^3=A\cdot 33^2{3}^3$$
311	310	oveq2d	$$⊢\phi \to A^{2}3A{3}^2{3}^3=A^{2}A\cdot 33^2{3}^3$$
312	307 311	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^{2}A\cdot 33^2{3}^3$$
313	8 3	mulcld	$$⊢\phi \to A\cdot 3\in ℂ$$
314	313 11 6	mulassd	$$⊢\phi \to A\cdot 33^2{3}^3=A\cdot 33^2{3}^3$$
315	314	oveq2d	$$⊢\phi \to A^{2}A\cdot 33^2{3}^3=A^{2}A\cdot 33^2{3}^3$$
316	312 315	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^{2}A\cdot 33^2{3}^3$$
317	11 6	mulcld	$$⊢\phi \to 3^2{3}^3\in ℂ$$
318	8 3 317	mulassd	$$⊢\phi \to A\cdot 33^2{3}^3=A33^2{3}^3$$
319	318	oveq2d	$$⊢\phi \to A^{2}A\cdot 33^2{3}^3=A^{2}A33^2{3}^3$$
320	316 319	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2=A^{2}A33^2{3}^3$$
321	320	oveq1d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^{2}A33^2{3}^3+A3{3^{2}A}^2\cdot 3$$
322	3 317	mulcld	$$⊢\phi \to 33^2{3}^3\in ℂ$$
323	9 8 322	mulassd	$$⊢\phi \to A^{2}A33^2{3}^3=A^{2}A33^2{3}^3$$
324	323	oveq1d	$$⊢\phi \to A^{2}A33^2{3}^3+A3{3^{2}A}^2\cdot 3=A^{2}A33^2{3}^3+A3{3^{2}A}^2\cdot 3$$
325	321 324	eqtr4d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^{2}A33^2{3}^3+A3{3^{2}A}^2\cdot 3$$
326	8 29	expp1d	$$⊢\phi \to A^{2+1}=A^{2}A$$
327	326	eqcomd	$$⊢\phi \to A^{2}A=A^{2+1}$$
328	327	oveq1d	$$⊢\phi \to A^{2}A33^2{3}^3=A^{2+1}33^2{3}^3$$
329	328	oveq1d	$$⊢\phi \to A^{2}A33^2{3}^3+A3{3^{2}A}^2\cdot 3=A^{2+1}33^2{3}^3+A3{3^{2}A}^2\cdot 3$$
330	325 329	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^{2+1}33^2{3}^3+A3{3^{2}A}^2\cdot 3$$
331		2p1e3	$$⊢2+1=3$$
332	331	a1i	$$⊢\phi \to 2+1=3$$
333	332	oveq2d	$$⊢\phi \to A^{2+1}=A^3$$
334	333	oveq1d	$$⊢\phi \to A^{2+1}33^2{3}^3=A^{3}33^2{3}^3$$
335	334	oveq1d	$$⊢\phi \to A^{2+1}33^2{3}^3+A3{3^{2}A}^2\cdot 3=A^{3}33^2{3}^3+A3{3^{2}A}^2\cdot 3$$
336	330 335	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^{3}33^2{3}^3+A3{3^{2}A}^2\cdot 3$$
337	3 5 29	expaddd	$$⊢\phi \to 3^{2+3}=3^2{3}^3$$
338	337	oveq2d	$$⊢\phi \to 33^{2+3}=33^2{3}^3$$
339	338	eqcomd	$$⊢\phi \to 33^2{3}^3=33^{2+3}$$
340	29 5	nn0addcld	$$⊢\phi \to 2+3\in {\mathbb{N}}_0$$
341	3 340	expcld	$$⊢\phi \to 3^{2+3}\in ℂ$$
342	3 341	mulcomd	$$⊢\phi \to 33^{2+3}=3^{2+3}\cdot 3$$
343	339 342	eqtrd	$$⊢\phi \to 33^2{3}^3=3^{2+3}\cdot 3$$
344	3 340	expp1d	$$⊢\phi \to 3^{2+3+1}=3^{2+3}\cdot 3$$
345	343 344	eqtr4d	$$⊢\phi \to 33^2{3}^3=3^{2+3+1}$$
346	345	oveq2d	$$⊢\phi \to A^{3}33^2{3}^3=A^3{3}^{2+3+1}$$
347	346	oveq1d	$$⊢\phi \to A^{3}33^2{3}^3+A3{3^{2}A}^2\cdot 3=A^3{3}^{2+3+1}+A3{3^{2}A}^2\cdot 3$$
348	336 347	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^{2+3+1}+A3{3^{2}A}^2\cdot 3$$
349	332	oveq2d	$$⊢\phi \to 2+2+1=2+3$$
350	349	oveq1d	$$⊢\phi \to 2+\left(2+1\right)+1=2+3+1$$
351	350	oveq2d	$$⊢\phi \to 3^{2+\left(2+1\right)+1}=3^{2+3+1}$$
352	351	oveq2d	$$⊢\phi \to A^3{3}^{2+\left(2+1\right)+1}=A^3{3}^{2+3+1}$$
353	352	oveq1d	$$⊢\phi \to A^3{3}^{2+\left(2+1\right)+1}+A3{3^{2}A}^2\cdot 3=A^3{3}^{2+3+1}+A3{3^{2}A}^2\cdot 3$$
354	348 353	eqtr4d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^{2+\left(2+1\right)+1}+A3{3^{2}A}^2\cdot 3$$
355	29	nn0cnd	$$⊢\phi \to 2\in ℂ$$
356		ax-1cn	$$⊢1\in ℂ$$
357	356	a1i	$$⊢\phi \to 1\in ℂ$$
358	355 355 357	addassd	$$⊢\phi \to 2+2+1=2+2+1$$
359	358	oveq1d	$$⊢\phi \to \left(2+2\right)+1+1=2+\left(2+1\right)+1$$
360	359	oveq2d	$$⊢\phi \to 3^{\left(2+2\right)+1+1}=3^{2+\left(2+1\right)+1}$$
361	360	oveq2d	$$⊢\phi \to A^3{3}^{\left(2+2\right)+1+1}=A^3{3}^{2+\left(2+1\right)+1}$$
362	361	oveq1d	$$⊢\phi \to A^3{3}^{\left(2+2\right)+1+1}+A3{3^{2}A}^2\cdot 3=A^3{3}^{2+\left(2+1\right)+1}+A3{3^{2}A}^2\cdot 3$$
363	354 362	eqtr4d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^{\left(2+2\right)+1+1}+A3{3^{2}A}^2\cdot 3$$
364	266	oveq1d	$$⊢\phi \to \left(2+2\right)+1+1=4+1+1$$
365	364	oveq2d	$$⊢\phi \to 3^{\left(2+2\right)+1+1}=3^{4+1+1}$$
366	365	oveq2d	$$⊢\phi \to A^3{3}^{\left(2+2\right)+1+1}=A^3{3}^{4+1+1}$$
367	366	oveq1d	$$⊢\phi \to A^3{3}^{\left(2+2\right)+1+1}+A3{3^{2}A}^2\cdot 3=A^3{3}^{4+1+1}+A3{3^{2}A}^2\cdot 3$$
368	363 367	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^{4+1+1}+A3{3^{2}A}^2\cdot 3$$
369	271	oveq1d	$$⊢\phi \to 4+1+1=5+1$$
370	369	oveq2d	$$⊢\phi \to 3^{4+1+1}=3^{5+1}$$
371	370	oveq2d	$$⊢\phi \to A^3{3}^{4+1+1}=A^3{3}^{5+1}$$
372	371	oveq1d	$$⊢\phi \to A^3{3}^{4+1+1}+A3{3^{2}A}^2\cdot 3=A^3{3}^{5+1}+A3{3^{2}A}^2\cdot 3$$
373	368 372	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^{5+1}+A3{3^{2}A}^2\cdot 3$$
374		5p1e6	$$⊢5+1=6$$
375	374	a1i	$$⊢\phi \to 5+1=6$$
376	375	oveq2d	$$⊢\phi \to 3^{5+1}=3^6$$
377	376	oveq2d	$$⊢\phi \to A^3{3}^{5+1}=A^3{3}^6$$
378	377	oveq1d	$$⊢\phi \to A^3{3}^{5+1}+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A3{3^{2}A}^2\cdot 3$$
379	373 378	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A3{3^{2}A}^2\cdot 3$$
380	11 8 29	mulexpd	$$⊢\phi \to {3^{2}A}^2={\left(3^2\right)}^2{A}^2$$
381	380	oveq1d	$$⊢\phi \to {3^{2}A}^2\cdot 3={\left(3^2\right)}^2{A}^2\cdot 3$$
382	381	oveq2d	$$⊢\phi \to 3{3^{2}A}^2\cdot 3=3{\left(3^2\right)}^2{A}^2\cdot 3$$
383	382	oveq2d	$$⊢\phi \to A3{3^{2}A}^2\cdot 3=A3{\left(3^2\right)}^2{A}^2\cdot 3$$
384	383	oveq2d	$$⊢\phi \to A^3{3}^6+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A3{\left(3^2\right)}^2{A}^2\cdot 3$$
385	379 384	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A3{\left(3^2\right)}^2{A}^2\cdot 3$$
386	11	sqcld	$$⊢\phi \to {\left(3^2\right)}^2\in ℂ$$
387	386 9	mulcld	$$⊢\phi \to {\left(3^2\right)}^2{A}^2\in ℂ$$
388	387 3	mulcld	$$⊢\phi \to {\left(3^2\right)}^2{A}^2\cdot 3\in ℂ$$
389	3 388	mulcld	$$⊢\phi \to 3{\left(3^2\right)}^2{A}^2\cdot 3\in ℂ$$
390	8 389	mulcomd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=3{\left(3^2\right)}^2{A}^2\cdot 3A$$
391	3 388	mulcomd	$$⊢\phi \to 3{\left(3^2\right)}^2{A}^2\cdot 3={\left(3^2\right)}^2{A}^2\cdot 3\cdot 3$$
392	391	oveq1d	$$⊢\phi \to 3{\left(3^2\right)}^2{A}^2\cdot 3A={\left(3^2\right)}^2{A}^2\cdot 3\cdot 3A$$
393	390 392	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3={\left(3^2\right)}^2{A}^2\cdot 3\cdot 3A$$
394	386 9	mulcomd	$$⊢\phi \to {\left(3^2\right)}^2{A}^2=A^2{\left(3^2\right)}^2$$
395	394	oveq1d	$$⊢\phi \to {\left(3^2\right)}^2{A}^2\cdot 3=A^2{\left(3^2\right)}^2\cdot 3$$
396	395	oveq1d	$$⊢\phi \to {\left(3^2\right)}^2{A}^2\cdot 3\cdot 3=A^2{\left(3^2\right)}^2\cdot 3\cdot 3$$
397	396	oveq1d	$$⊢\phi \to {\left(3^2\right)}^2{A}^2\cdot 3\cdot 3A=A^2{\left(3^2\right)}^2\cdot 3\cdot 3A$$
398	393 397	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^2{\left(3^2\right)}^2\cdot 3\cdot 3A$$
399	9 386	mulcld	$$⊢\phi \to A^2{\left(3^2\right)}^2\in ℂ$$
400	399 3	mulcld	$$⊢\phi \to A^2{\left(3^2\right)}^2\cdot 3\in ℂ$$
401	400 3 8	mulassd	$$⊢\phi \to A^2{\left(3^2\right)}^2\cdot 3\cdot 3A=A^2{\left(3^2\right)}^2\cdot 33A$$
402	398 401	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^2{\left(3^2\right)}^2\cdot 33A$$
403	399 3 295	mulassd	$$⊢\phi \to A^2{\left(3^2\right)}^2\cdot 33A=A^2{\left(3^2\right)}^{2}33A$$
404	402 403	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^2{\left(3^2\right)}^{2}33A$$
405	3 295	mulcld	$$⊢\phi \to 33A\in ℂ$$
406	9 386 405	mulassd	$$⊢\phi \to A^2{\left(3^2\right)}^{2}33A=A^2{\left(3^2\right)}^{2}33A$$
407	404 406	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^2{\left(3^2\right)}^{2}33A$$
408	386 405	mulcomd	$$⊢\phi \to {\left(3^2\right)}^{2}33A=33A{\left(3^2\right)}^2$$
409	408	oveq2d	$$⊢\phi \to A^2{\left(3^2\right)}^{2}33A=A^{2}33A{\left(3^2\right)}^2$$
410	407 409	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^{2}33A{\left(3^2\right)}^2$$
411	3 295	mulcomd	$$⊢\phi \to 33A=3A\cdot 3$$
412	411	oveq1d	$$⊢\phi \to 33A{\left(3^2\right)}^2=3A\cdot 3{\left(3^2\right)}^2$$
413	412	oveq2d	$$⊢\phi \to A^{2}33A{\left(3^2\right)}^2=A^{2}3A\cdot 3{\left(3^2\right)}^2$$
414	410 413	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^{2}3A\cdot 3{\left(3^2\right)}^2$$
415	308	oveq1d	$$⊢\phi \to 3A\cdot 3=A\cdot 3\cdot 3$$
416	415	oveq1d	$$⊢\phi \to 3A\cdot 3{\left(3^2\right)}^2=A\cdot 3\cdot 3{\left(3^2\right)}^2$$
417	416	oveq2d	$$⊢\phi \to A^{2}3A\cdot 3{\left(3^2\right)}^2=A^{2}A\cdot 3\cdot 3{\left(3^2\right)}^2$$
418	414 417	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^{2}A\cdot 3\cdot 3{\left(3^2\right)}^2$$
419	313 3 386	mulassd	$$⊢\phi \to A\cdot 3\cdot 3{\left(3^2\right)}^2=A\cdot 33{\left(3^2\right)}^2$$
420	419	oveq2d	$$⊢\phi \to A^{2}A\cdot 3\cdot 3{\left(3^2\right)}^2=A^{2}A\cdot 33{\left(3^2\right)}^2$$
421	418 420	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^{2}A\cdot 33{\left(3^2\right)}^2$$
422	3 386	mulcld	$$⊢\phi \to 3{\left(3^2\right)}^2\in ℂ$$
423	8 3 422	mulassd	$$⊢\phi \to A\cdot 33{\left(3^2\right)}^2=A33{\left(3^2\right)}^2$$
424	423	oveq2d	$$⊢\phi \to A^{2}A\cdot 33{\left(3^2\right)}^2=A^{2}A33{\left(3^2\right)}^2$$
425	421 424	eqtrd	$$⊢\phi \to A3{\left(3^2\right)}^2{A}^2\cdot 3=A^{2}A33{\left(3^2\right)}^2$$
426	425	oveq2d	$$⊢\phi \to A^3{3}^6+A3{\left(3^2\right)}^2{A}^2\cdot 3=A^3{3}^6+A^{2}A33{\left(3^2\right)}^2$$
427	385 426	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A^{2}A33{\left(3^2\right)}^2$$
428	3 422	mulcld	$$⊢\phi \to 33{\left(3^2\right)}^2\in ℂ$$
429	9 8 428	mulassd	$$⊢\phi \to A^{2}A33{\left(3^2\right)}^2=A^{2}A33{\left(3^2\right)}^2$$
430	429	oveq2d	$$⊢\phi \to A^3{3}^6+A^{2}A33{\left(3^2\right)}^2=A^3{3}^6+A^{2}A33{\left(3^2\right)}^2$$
431	427 430	eqtr4d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A^{2}A33{\left(3^2\right)}^2$$
432	327	oveq1d	$$⊢\phi \to A^{2}A33{\left(3^2\right)}^2=A^{2+1}33{\left(3^2\right)}^2$$
433	432	oveq2d	$$⊢\phi \to A^3{3}^6+A^{2}A33{\left(3^2\right)}^2=A^3{3}^6+A^{2+1}33{\left(3^2\right)}^2$$
434	431 433	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A^{2+1}33{\left(3^2\right)}^2$$
435	333	oveq1d	$$⊢\phi \to A^{2+1}33{\left(3^2\right)}^2=A^{3}33{\left(3^2\right)}^2$$
436	435	oveq2d	$$⊢\phi \to A^3{3}^6+A^{2+1}33{\left(3^2\right)}^2=A^3{3}^6+A^{3}33{\left(3^2\right)}^2$$
437	434 436	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3{3}^6+A^{3}33{\left(3^2\right)}^2$$
438	8 5	expcld	$$⊢\phi \to A^3\in ℂ$$
439		6nn0	$$⊢6\in {\mathbb{N}}_0$$
440	439	a1i	$$⊢\phi \to 6\in {\mathbb{N}}_0$$
441	3 440	expcld	$$⊢\phi \to 3^6\in ℂ$$
442	438 441 428	adddid	$$⊢\phi \to A^3\left(3^6+33{\left(3^2\right)}^2\right)=A^3{3}^6+A^{3}33{\left(3^2\right)}^2$$
443	442	eqcomd	$$⊢\phi \to A^3{3}^6+A^{3}33{\left(3^2\right)}^2=A^3\left(3^6+33{\left(3^2\right)}^2\right)$$
444	437 443	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3\left(3^6+33{\left(3^2\right)}^2\right)$$
445	3 29 29	expmuld	$$⊢\phi \to 3^{2\cdot 2}={\left(3^2\right)}^2$$
446	445	oveq2d	$$⊢\phi \to 33^{2\cdot 2}=3{\left(3^2\right)}^2$$
447	446	oveq2d	$$⊢\phi \to 333^{2\cdot 2}=33{\left(3^2\right)}^2$$
448	447	eqcomd	$$⊢\phi \to 33{\left(3^2\right)}^2=333^{2\cdot 2}$$
449	29 29	nn0mulcld	$$⊢\phi \to 2\cdot 2\in {\mathbb{N}}_0$$
450	3 449	expcld	$$⊢\phi \to 3^{2\cdot 2}\in ℂ$$
451	3 450	mulcomd	$$⊢\phi \to 33^{2\cdot 2}=3^{2\cdot 2}\cdot 3$$
452	451	oveq2d	$$⊢\phi \to 333^{2\cdot 2}=33^{2\cdot 2}\cdot 3$$
453	448 452	eqtrd	$$⊢\phi \to 33{\left(3^2\right)}^2=33^{2\cdot 2}\cdot 3$$
454	3 449	expp1d	$$⊢\phi \to 3^{2\cdot 2+1}=3^{2\cdot 2}\cdot 3$$
455	454	oveq2d	$$⊢\phi \to 33^{2\cdot 2+1}=33^{2\cdot 2}\cdot 3$$
456	453 455	eqtr4d	$$⊢\phi \to 33{\left(3^2\right)}^2=33^{2\cdot 2+1}$$
457		1nn0	$$⊢1\in {\mathbb{N}}_0$$
458	457	a1i	$$⊢\phi \to 1\in {\mathbb{N}}_0$$
459	449 458	nn0addcld	$$⊢\phi \to 2\cdot 2+1\in {\mathbb{N}}_0$$
460	3 459	expcld	$$⊢\phi \to 3^{2\cdot 2+1}\in ℂ$$
461	3 460	mulcomd	$$⊢\phi \to 33^{2\cdot 2+1}=3^{2\cdot 2+1}\cdot 3$$
462	456 461	eqtrd	$$⊢\phi \to 33{\left(3^2\right)}^2=3^{2\cdot 2+1}\cdot 3$$
463	3 459	expp1d	$$⊢\phi \to 3^{2\cdot 2+1+1}=3^{2\cdot 2+1}\cdot 3$$
464	462 463	eqtr4d	$$⊢\phi \to 33{\left(3^2\right)}^2=3^{2\cdot 2+1+1}$$
465	464	oveq2d	$$⊢\phi \to 3^6+33{\left(3^2\right)}^2=3^6+3^{2\cdot 2+1+1}$$
466	465	oveq2d	$$⊢\phi \to A^3\left(3^6+33{\left(3^2\right)}^2\right)=A^3\left(3^6+3^{2\cdot 2+1+1}\right)$$
467	444 466	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3\left(3^6+3^{2\cdot 2+1+1}\right)$$
468		2t2e4	$$⊢2\cdot 2=4$$
469	468	a1i	$$⊢\phi \to 2\cdot 2=4$$
470	469	oveq1d	$$⊢\phi \to 2\cdot 2+1=4+1$$
471	470	oveq1d	$$⊢\phi \to 2\cdot 2+1+1=4+1+1$$
472	471	oveq2d	$$⊢\phi \to 3^{2\cdot 2+1+1}=3^{4+1+1}$$
473	472	oveq2d	$$⊢\phi \to 3^6+3^{2\cdot 2+1+1}=3^6+3^{4+1+1}$$
474	473	oveq2d	$$⊢\phi \to A^3\left(3^6+3^{2\cdot 2+1+1}\right)=A^3\left(3^6+3^{4+1+1}\right)$$
475	467 474	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3\left(3^6+3^{4+1+1}\right)$$
476	370	oveq2d	$$⊢\phi \to 3^6+3^{4+1+1}=3^6+3^{5+1}$$
477	476	oveq2d	$$⊢\phi \to A^3\left(3^6+3^{4+1+1}\right)=A^3\left(3^6+3^{5+1}\right)$$
478	475 477	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3\left(3^6+3^{5+1}\right)$$
479	376	oveq2d	$$⊢\phi \to 3^6+3^{5+1}=3^6+3^6$$
480	479	oveq2d	$$⊢\phi \to A^3\left(3^6+3^{5+1}\right)=A^3\left(3^6+3^6\right)$$
481	478 480	eqtrd	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3=A^3\left(3^6+3^6\right)$$
482	481	oveq1d	$$⊢\phi \to A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A^2{3}^5+A{3}^3=A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3$$
483	482	oveq2d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A^2{3}^5+A{3}^3\right)=A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)$$
484	483	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A^2{3}^5+A{3}^3\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)$$
485	484	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3\right)+\left(A^2{3}^5+A{3}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)\right)$$
486	485	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A33^3{A}^2{3}^2+A3{3^{2}A}^2\cdot 3+A^2{3}^5+A{3}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
487	281 486	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
488	8 34	mulcomd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=3\cdot 23^3{A}^2{3}^{2}A\cdot 3A$$
489	31 32	mulcomd	$$⊢\phi \to 3\cdot 23^3{A}^2{3}^{2}A=3^3{A}^2{3}^{2}A3\cdot 2$$
490	489	oveq1d	$$⊢\phi \to 3\cdot 23^3{A}^2{3}^{2}A\cdot 3=3^3{A}^2{3}^{2}A3\cdot 2\cdot 3$$
491	490	oveq1d	$$⊢\phi \to 3\cdot 23^3{A}^2{3}^{2}A\cdot 3A=3^3{A}^2{3}^{2}A3\cdot 2\cdot 3A$$
492	488 491	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=3^3{A}^2{3}^{2}A3\cdot 2\cdot 3A$$
493	286	oveq1d	$$⊢\phi \to 3^3{A}^2{3}^{2}A=A^2{3}^3{3}^{2}A$$
494	493	oveq1d	$$⊢\phi \to 3^3{A}^2{3}^{2}A3\cdot 2=A^2{3}^3{3}^{2}A3\cdot 2$$
495	494	oveq1d	$$⊢\phi \to 3^3{A}^2{3}^{2}A3\cdot 2\cdot 3=A^2{3}^3{3}^{2}A3\cdot 2\cdot 3$$
496	495	oveq1d	$$⊢\phi \to 3^3{A}^2{3}^{2}A3\cdot 2\cdot 3A=A^2{3}^3{3}^{2}A3\cdot 2\cdot 3A$$
497	492 496	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^2{3}^3{3}^{2}A3\cdot 2\cdot 3A$$
498	291 12	mulcld	$$⊢\phi \to A^2{3}^3{3}^{2}A\in ℂ$$
499	498 31	mulcld	$$⊢\phi \to A^2{3}^3{3}^{2}A3\cdot 2\in ℂ$$
500	499 3 8	mulassd	$$⊢\phi \to A^2{3}^3{3}^{2}A3\cdot 2\cdot 3A=A^2{3}^3{3}^{2}A3\cdot 23A$$
501	497 500	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^2{3}^3{3}^{2}A3\cdot 23A$$
502	498 31 295	mulassd	$$⊢\phi \to A^2{3}^3{3}^{2}A3\cdot 23A=A^2{3}^3{3}^{2}A3\cdot 23A$$
503	501 502	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^2{3}^3{3}^{2}A3\cdot 23A$$
504	31 295	mulcld	$$⊢\phi \to 3\cdot 23A\in ℂ$$
505	291 12 504	mulassd	$$⊢\phi \to A^2{3}^3{3}^{2}A3\cdot 23A=A^2{3}^3{3}^{2}A3\cdot 23A$$
506	503 505	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^2{3}^3{3}^{2}A3\cdot 23A$$
507	12 504	mulcld	$$⊢\phi \to 3^{2}A3\cdot 23A\in ℂ$$
508	9 6 507	mulassd	$$⊢\phi \to A^2{3}^3{3}^{2}A3\cdot 23A=A^2{3}^3{3}^{2}A3\cdot 23A$$
509	506 508	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^2{3}^3{3}^{2}A3\cdot 23A$$
510	6 507	mulcomd	$$⊢\phi \to 3^3{3}^{2}A3\cdot 23A=3^{2}A3\cdot 23A{3}^3$$
511	510	oveq2d	$$⊢\phi \to A^2{3}^3{3}^{2}A3\cdot 23A=A^2{3}^{2}A3\cdot 23A{3}^3$$
512	509 511	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^2{3}^{2}A3\cdot 23A{3}^3$$
513	232	oveq1d	$$⊢\phi \to 3^{2}A3\cdot 23A=A{3}^{2}3\cdot 23A$$
514	513	oveq1d	$$⊢\phi \to 3^{2}A3\cdot 23A{3}^3=A{3}^{2}3\cdot 23A{3}^3$$
515	514	oveq2d	$$⊢\phi \to A^2{3}^{2}A3\cdot 23A{3}^3=A^{2}A{3}^{2}3\cdot 23A{3}^3$$
516	512 515	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}A{3}^{2}3\cdot 23A{3}^3$$
517	237 504 6	mulassd	$$⊢\phi \to A{3}^{2}3\cdot 23A{3}^3=A{3}^{2}3\cdot 23A{3}^3$$
518	517	oveq2d	$$⊢\phi \to A^{2}A{3}^{2}3\cdot 23A{3}^3=A^{2}A{3}^{2}3\cdot 23A{3}^3$$
519	516 518	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}A{3}^{2}3\cdot 23A{3}^3$$
520	504 6	mulcld	$$⊢\phi \to 3\cdot 23A{3}^3\in ℂ$$
521	8 11 520	mulassd	$$⊢\phi \to A{3}^{2}3\cdot 23A{3}^3=A{3}^{2}3\cdot 23A{3}^3$$
522	521	oveq2d	$$⊢\phi \to A^{2}A{3}^{2}3\cdot 23A{3}^3=A^{2}A{3}^{2}3\cdot 23A{3}^3$$
523	519 522	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}A{3}^{2}3\cdot 23A{3}^3$$
524	11 520	mulcomd	$$⊢\phi \to 3^{2}3\cdot 23A{3}^3=3\cdot 23A{3}^3{3}^2$$
525	524	oveq2d	$$⊢\phi \to A{3}^{2}3\cdot 23A{3}^3=A3\cdot 23A{3}^3{3}^2$$
526	525	oveq2d	$$⊢\phi \to A^{2}A{3}^{2}3\cdot 23A{3}^3=A^{2}A3\cdot 23A{3}^3{3}^2$$
527	523 526	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}A3\cdot 23A{3}^3{3}^2$$
528	31 295	mulcomd	$$⊢\phi \to 3\cdot 23A=3A3\cdot 2$$
529	528	oveq1d	$$⊢\phi \to 3\cdot 23A{3}^3=3A3\cdot 23^3$$
530	529	oveq1d	$$⊢\phi \to 3\cdot 23A{3}^3{3}^2=3A3\cdot 23^3{3}^2$$
531	530	oveq2d	$$⊢\phi \to A3\cdot 23A{3}^3{3}^2=A3A3\cdot 23^3{3}^2$$
532	531	oveq2d	$$⊢\phi \to A^{2}A3\cdot 23A{3}^3{3}^2=A^{2}A3A3\cdot 23^3{3}^2$$
533	527 532	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}A3A3\cdot 23^3{3}^2$$
534	308	oveq1d	$$⊢\phi \to 3A3\cdot 2=A\cdot 33\cdot 2$$
535	534	oveq1d	$$⊢\phi \to 3A3\cdot 23^3=A\cdot 33\cdot 23^3$$
536	535	oveq1d	$$⊢\phi \to 3A3\cdot 23^3{3}^2=A\cdot 33\cdot 23^3{3}^2$$
537	536	oveq2d	$$⊢\phi \to A3A3\cdot 23^3{3}^2=AA\cdot 33\cdot 23^3{3}^2$$
538	537	oveq2d	$$⊢\phi \to A^{2}A3A3\cdot 23^3{3}^2=A^{2}AA\cdot 33\cdot 23^3{3}^2$$
539	533 538	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}AA\cdot 33\cdot 23^3{3}^2$$
540	313 31	mulcld	$$⊢\phi \to A\cdot 33\cdot 2\in ℂ$$
541	540 6 11	mulassd	$$⊢\phi \to A\cdot 33\cdot 23^3{3}^2=A\cdot 33\cdot 23^3{3}^2$$
542	541	oveq2d	$$⊢\phi \to AA\cdot 33\cdot 23^3{3}^2=AA\cdot 33\cdot 23^3{3}^2$$
543	542	oveq2d	$$⊢\phi \to A^{2}AA\cdot 33\cdot 23^3{3}^2=A^{2}AA\cdot 33\cdot 23^3{3}^2$$
544	539 543	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}AA\cdot 33\cdot 23^3{3}^2$$
545	6 11	mulcld	$$⊢\phi \to 3^3{3}^2\in ℂ$$
546	313 31 545	mulassd	$$⊢\phi \to A\cdot 33\cdot 23^3{3}^2=A\cdot 33\cdot 23^3{3}^2$$
547	546	oveq2d	$$⊢\phi \to AA\cdot 33\cdot 23^3{3}^2=AA\cdot 33\cdot 23^3{3}^2$$
548	547	oveq2d	$$⊢\phi \to A^{2}AA\cdot 33\cdot 23^3{3}^2=A^{2}AA\cdot 33\cdot 23^3{3}^2$$
549	544 548	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}AA\cdot 33\cdot 23^3{3}^2$$
550	31 545	mulcld	$$⊢\phi \to 3\cdot 23^3{3}^2\in ℂ$$
551	8 3 550	mulassd	$$⊢\phi \to A\cdot 33\cdot 23^3{3}^2=A33\cdot 23^3{3}^2$$
552	551	oveq2d	$$⊢\phi \to AA\cdot 33\cdot 23^3{3}^2=AA33\cdot 23^3{3}^2$$
553	552	oveq2d	$$⊢\phi \to A^{2}AA\cdot 33\cdot 23^3{3}^2=A^{2}AA33\cdot 23^3{3}^2$$
554	549 553	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}AA33\cdot 23^3{3}^2$$
555	3 355 545	mulassd	$$⊢\phi \to 3\cdot 23^3{3}^2=323^3{3}^2$$
556	555	oveq2d	$$⊢\phi \to 33\cdot 23^3{3}^2=3323^3{3}^2$$
557	556	oveq2d	$$⊢\phi \to A33\cdot 23^3{3}^2=A3323^3{3}^2$$
558	557	oveq2d	$$⊢\phi \to AA33\cdot 23^3{3}^2=AA3323^3{3}^2$$
559	558	oveq2d	$$⊢\phi \to A^{2}AA33\cdot 23^3{3}^2=A^{2}AA3323^3{3}^2$$
560	554 559	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3=A^{2}AA3323^3{3}^2$$
561	560	oveq1d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{2}AA3323^3{3}^2+A{3^{2}A}^3$$
562	355 545	mulcld	$$⊢\phi \to 23^3{3}^2\in ℂ$$
563	3 562	mulcld	$$⊢\phi \to 323^3{3}^2\in ℂ$$
564	3 563	mulcld	$$⊢\phi \to 3323^3{3}^2\in ℂ$$
565	8 564	mulcld	$$⊢\phi \to A3323^3{3}^2\in ℂ$$
566	9 8 565	mulassd	$$⊢\phi \to A^{2}AA3323^3{3}^2=A^{2}AA3323^3{3}^2$$
567	566	oveq1d	$$⊢\phi \to A^{2}AA3323^3{3}^2+A{3^{2}A}^3=A^{2}AA3323^3{3}^2+A{3^{2}A}^3$$
568	561 567	eqtr4d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{2}AA3323^3{3}^2+A{3^{2}A}^3$$
569	9 8	mulcld	$$⊢\phi \to A^{2}A\in ℂ$$
570	569 8 564	mulassd	$$⊢\phi \to A^{2}AA3323^3{3}^2=A^{2}AA3323^3{3}^2$$
571	570	oveq1d	$$⊢\phi \to A^{2}AA3323^3{3}^2+A{3^{2}A}^3=A^{2}AA3323^3{3}^2+A{3^{2}A}^3$$
572	568 571	eqtr4d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{2}AA3323^3{3}^2+A{3^{2}A}^3$$
573	327	oveq1d	$$⊢\phi \to A^{2}AA=A^{2+1}A$$
574	29 458	nn0addcld	$$⊢\phi \to 2+1\in {\mathbb{N}}_0$$
575	8 574	expp1d	$$⊢\phi \to A^{2+1+1}=A^{2+1}A$$
576	573 575	eqtr4d	$$⊢\phi \to A^{2}AA=A^{2+1+1}$$
577	576	oveq1d	$$⊢\phi \to A^{2}AA3323^3{3}^2=A^{2+1+1}3323^3{3}^2$$
578	577	oveq1d	$$⊢\phi \to A^{2}AA3323^3{3}^2+A{3^{2}A}^3=A^{2+1+1}3323^3{3}^2+A{3^{2}A}^3$$
579	572 578	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{2+1+1}3323^3{3}^2+A{3^{2}A}^3$$
580	332	oveq1d	$$⊢\phi \to 2+1+1=3+1$$
581	580	oveq2d	$$⊢\phi \to A^{2+1+1}=A^{3+1}$$
582	581	oveq1d	$$⊢\phi \to A^{2+1+1}3323^3{3}^2=A^{3+1}3323^3{3}^2$$
583	582	oveq1d	$$⊢\phi \to A^{2+1+1}3323^3{3}^2+A{3^{2}A}^3=A^{3+1}3323^3{3}^2+A{3^{2}A}^3$$
584	579 583	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{3+1}3323^3{3}^2+A{3^{2}A}^3$$
585		3p1e4	$$⊢3+1=4$$
586	585	a1i	$$⊢\phi \to 3+1=4$$
587	586	oveq2d	$$⊢\phi \to A^{3+1}=A^4$$
588	587	oveq1d	$$⊢\phi \to A^{3+1}3323^3{3}^2=A^{4}3323^3{3}^2$$
589	588	oveq1d	$$⊢\phi \to A^{3+1}3323^3{3}^2+A{3^{2}A}^3=A^{4}3323^3{3}^2+A{3^{2}A}^3$$
590	584 589	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{4}3323^3{3}^2+A{3^{2}A}^3$$
591	3 29 5	expaddd	$$⊢\phi \to 3^{3+2}=3^3{3}^2$$
592	591	oveq2d	$$⊢\phi \to 23^{3+2}=23^3{3}^2$$
593	592	oveq2d	$$⊢\phi \to 323^{3+2}=323^3{3}^2$$
594	593	oveq2d	$$⊢\phi \to 3323^{3+2}=3323^3{3}^2$$
595	594	eqcomd	$$⊢\phi \to 3323^3{3}^2=3323^{3+2}$$
596	595	oveq2d	$$⊢\phi \to A^{4}3323^3{3}^2=A^{4}3323^{3+2}$$
597	596	oveq1d	$$⊢\phi \to A^{4}3323^3{3}^2+A{3^{2}A}^3=A^{4}3323^{3+2}+A{3^{2}A}^3$$
598	590 597	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{4}3323^{3+2}+A{3^{2}A}^3$$
599		3p2e5	$$⊢3+2=5$$
600	599	a1i	$$⊢\phi \to 3+2=5$$
601	600	oveq2d	$$⊢\phi \to 3^{3+2}=3^5$$
602	601	oveq2d	$$⊢\phi \to 23^{3+2}=23^5$$
603	602	oveq2d	$$⊢\phi \to 323^{3+2}=323^5$$
604	603	oveq2d	$$⊢\phi \to 3323^{3+2}=3323^5$$
605	604	oveq2d	$$⊢\phi \to A^{4}3323^{3+2}=A^{4}3323^5$$
606	605	oveq1d	$$⊢\phi \to A^{4}3323^{3+2}+A{3^{2}A}^3=A^{4}3323^5+A{3^{2}A}^3$$
607	598 606	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{4}3323^5+A{3^{2}A}^3$$
608		5nn0	$$⊢5\in {\mathbb{N}}_0$$
609	608	a1i	$$⊢\phi \to 5\in {\mathbb{N}}_0$$
610	3 609	expcld	$$⊢\phi \to 3^5\in ℂ$$
611	355 610	mulcomd	$$⊢\phi \to 23^5=3^5\cdot 2$$
612	611	oveq2d	$$⊢\phi \to 323^5=33^5\cdot 2$$
613	612	oveq2d	$$⊢\phi \to 3323^5=333^5\cdot 2$$
614	613	oveq2d	$$⊢\phi \to A^{4}3323^5=A^{4}333^5\cdot 2$$
615	614	oveq1d	$$⊢\phi \to A^{4}3323^5+A{3^{2}A}^3=A^{4}333^5\cdot 2+A{3^{2}A}^3$$
616	607 615	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{4}333^5\cdot 2+A{3^{2}A}^3$$
617	3 610 355	mulassd	$$⊢\phi \to 33^5\cdot 2=33^5\cdot 2$$
618	617	oveq2d	$$⊢\phi \to 333^5\cdot 2=333^5\cdot 2$$
619	618	oveq2d	$$⊢\phi \to A^{4}333^5\cdot 2=A^{4}333^5\cdot 2$$
620	619	oveq1d	$$⊢\phi \to A^{4}333^5\cdot 2+A{3^{2}A}^3=A^{4}333^5\cdot 2+A{3^{2}A}^3$$
621	616 620	eqtr4d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{4}333^5\cdot 2+A{3^{2}A}^3$$
622	3 610	mulcld	$$⊢\phi \to 33^5\in ℂ$$
623	3 622 355	mulassd	$$⊢\phi \to 333^5\cdot 2=333^5\cdot 2$$
624	623	oveq2d	$$⊢\phi \to A^{4}333^5\cdot 2=A^{4}333^5\cdot 2$$
625	624	oveq1d	$$⊢\phi \to A^{4}333^5\cdot 2+A{3^{2}A}^3=A^{4}333^5\cdot 2+A{3^{2}A}^3$$
626	621 625	eqtr4d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^{4}333^5\cdot 2+A{3^{2}A}^3$$
627	3 610	mulcomd	$$⊢\phi \to 33^5=3^5\cdot 3$$
628	627	oveq2d	$$⊢\phi \to 333^5=33^5\cdot 3$$
629	3 609	expp1d	$$⊢\phi \to 3^{5+1}=3^5\cdot 3$$
630	629	oveq2d	$$⊢\phi \to 33^{5+1}=33^5\cdot 3$$
631	628 630	eqtr4d	$$⊢\phi \to 333^5=33^{5+1}$$
632	609 458	nn0addcld	$$⊢\phi \to 5+1\in {\mathbb{N}}_0$$
633	3 632	expcld	$$⊢\phi \to 3^{5+1}\in ℂ$$
634	3 633	mulcomd	$$⊢\phi \to 33^{5+1}=3^{5+1}\cdot 3$$
635	631 634	eqtrd	$$⊢\phi \to 333^5=3^{5+1}\cdot 3$$
636	3 632	expp1d	$$⊢\phi \to 3^{5+1+1}=3^{5+1}\cdot 3$$
637	635 636	eqtr4d	$$⊢\phi \to 333^5=3^{5+1+1}$$
638	637	oveq1d	$$⊢\phi \to 333^5\cdot 2=3^{5+1+1}\cdot 2$$
639	638	oveq2d	$$⊢\phi \to A^{4}333^5\cdot 2=A^4{3}^{5+1+1}\cdot 2$$
640	639	oveq1d	$$⊢\phi \to A^{4}333^5\cdot 2+A{3^{2}A}^3=A^4{3}^{5+1+1}\cdot 2+A{3^{2}A}^3$$
641	626 640	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^{5+1+1}\cdot 2+A{3^{2}A}^3$$
642	375	oveq1d	$$⊢\phi \to 5+1+1=6+1$$
643	642	oveq2d	$$⊢\phi \to 3^{5+1+1}=3^{6+1}$$
644	643	oveq1d	$$⊢\phi \to 3^{5+1+1}\cdot 2=3^{6+1}\cdot 2$$
645	644	oveq2d	$$⊢\phi \to A^4{3}^{5+1+1}\cdot 2=A^4{3}^{6+1}\cdot 2$$
646	645	oveq1d	$$⊢\phi \to A^4{3}^{5+1+1}\cdot 2+A{3^{2}A}^3=A^4{3}^{6+1}\cdot 2+A{3^{2}A}^3$$
647	641 646	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^{6+1}\cdot 2+A{3^{2}A}^3$$
648		6p1e7	$$⊢6+1=7$$
649	648	a1i	$$⊢\phi \to 6+1=7$$
650	649	oveq2d	$$⊢\phi \to 3^{6+1}=3^7$$
651	650	oveq1d	$$⊢\phi \to 3^{6+1}\cdot 2=3^7\cdot 2$$
652	651	oveq2d	$$⊢\phi \to A^4{3}^{6+1}\cdot 2=A^4{3}^7\cdot 2$$
653	652	oveq1d	$$⊢\phi \to A^4{3}^{6+1}\cdot 2+A{3^{2}A}^3=A^4{3}^7\cdot 2+A{3^{2}A}^3$$
654	647 653	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A{3^{2}A}^3$$
655	11 8 5	mulexpd	$$⊢\phi \to {3^{2}A}^3={\left(3^2\right)}^3{A}^3$$
656	655	oveq2d	$$⊢\phi \to A{3^{2}A}^3=A{\left(3^2\right)}^3{A}^3$$
657	656	oveq2d	$$⊢\phi \to A^4{3}^7\cdot 2+A{3^{2}A}^3=A^4{3}^7\cdot 2+A{\left(3^2\right)}^3{A}^3$$
658	654 657	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A{\left(3^2\right)}^3{A}^3$$
659	11 5	expcld	$$⊢\phi \to {\left(3^2\right)}^3\in ℂ$$
660	659 438	mulcld	$$⊢\phi \to {\left(3^2\right)}^3{A}^3\in ℂ$$
661	8 660	mulcomd	$$⊢\phi \to A{\left(3^2\right)}^3{A}^3={\left(3^2\right)}^3{A}^{3}A$$
662	659 438	mulcomd	$$⊢\phi \to {\left(3^2\right)}^3{A}^3=A^3{\left(3^2\right)}^3$$
663	662	oveq1d	$$⊢\phi \to {\left(3^2\right)}^3{A}^{3}A=A^3{\left(3^2\right)}^{3}A$$
664	661 663	eqtrd	$$⊢\phi \to A{\left(3^2\right)}^3{A}^3=A^3{\left(3^2\right)}^{3}A$$
665	438 659 8	mulassd	$$⊢\phi \to A^3{\left(3^2\right)}^{3}A=A^3{\left(3^2\right)}^{3}A$$
666	664 665	eqtrd	$$⊢\phi \to A{\left(3^2\right)}^3{A}^3=A^3{\left(3^2\right)}^{3}A$$
667	659 8	mulcomd	$$⊢\phi \to {\left(3^2\right)}^{3}A=A{\left(3^2\right)}^3$$
668	667	oveq2d	$$⊢\phi \to A^3{\left(3^2\right)}^{3}A=A^{3}A{\left(3^2\right)}^3$$
669	666 668	eqtrd	$$⊢\phi \to A{\left(3^2\right)}^3{A}^3=A^{3}A{\left(3^2\right)}^3$$
670	669	oveq2d	$$⊢\phi \to A^4{3}^7\cdot 2+A{\left(3^2\right)}^3{A}^3=A^4{3}^7\cdot 2+A^{3}A{\left(3^2\right)}^3$$
671	658 670	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A^{3}A{\left(3^2\right)}^3$$
672	438 8 659	mulassd	$$⊢\phi \to A^{3}A{\left(3^2\right)}^3=A^{3}A{\left(3^2\right)}^3$$
673	672	oveq2d	$$⊢\phi \to A^4{3}^7\cdot 2+A^{3}A{\left(3^2\right)}^3=A^4{3}^7\cdot 2+A^{3}A{\left(3^2\right)}^3$$
674	671 673	eqtr4d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A^{3}A{\left(3^2\right)}^3$$
675	8 5	expp1d	$$⊢\phi \to A^{3+1}=A^{3}A$$
676	675	eqcomd	$$⊢\phi \to A^{3}A=A^{3+1}$$
677	676	oveq1d	$$⊢\phi \to A^{3}A{\left(3^2\right)}^3=A^{3+1}{\left(3^2\right)}^3$$
678	677	oveq2d	$$⊢\phi \to A^4{3}^7\cdot 2+A^{3}A{\left(3^2\right)}^3=A^4{3}^7\cdot 2+A^{3+1}{\left(3^2\right)}^3$$
679	674 678	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A^{3+1}{\left(3^2\right)}^3$$
680	587	oveq1d	$$⊢\phi \to A^{3+1}{\left(3^2\right)}^3=A^4{\left(3^2\right)}^3$$
681	680	oveq2d	$$⊢\phi \to A^4{3}^7\cdot 2+A^{3+1}{\left(3^2\right)}^3=A^4{3}^7\cdot 2+A^4{\left(3^2\right)}^3$$
682	679 681	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A^4{\left(3^2\right)}^3$$
683	3 5 29	expmuld	$$⊢\phi \to 3^{2\cdot 3}={\left(3^2\right)}^3$$
684	683	eqcomd	$$⊢\phi \to {\left(3^2\right)}^3=3^{2\cdot 3}$$
685	684	oveq2d	$$⊢\phi \to A^4{\left(3^2\right)}^3=A^4{3}^{2\cdot 3}$$
686	685	oveq2d	$$⊢\phi \to A^4{3}^7\cdot 2+A^4{\left(3^2\right)}^3=A^4{3}^7\cdot 2+A^4{3}^{2\cdot 3}$$
687	682 686	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A^4{3}^{2\cdot 3}$$
688		2cn	$$⊢2\in ℂ$$
689		3t2e6	$$⊢3\cdot 2=6$$
690	2 688 689	mulcomli	$$⊢2\cdot 3=6$$
691	690	a1i	$$⊢\phi \to 2\cdot 3=6$$
692	691	oveq2d	$$⊢\phi \to 3^{2\cdot 3}=3^6$$
693	692	oveq2d	$$⊢\phi \to A^4{3}^{2\cdot 3}=A^4{3}^6$$
694	693	oveq2d	$$⊢\phi \to A^4{3}^7\cdot 2+A^4{3}^{2\cdot 3}=A^4{3}^7\cdot 2+A^4{3}^6$$
695	687 694	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4{3}^7\cdot 2+A^4{3}^6$$
696		4nn0	$$⊢4\in {\mathbb{N}}_0$$
697	696	a1i	$$⊢\phi \to 4\in {\mathbb{N}}_0$$
698	8 697	expcld	$$⊢\phi \to A^4\in ℂ$$
699		7nn0	$$⊢7\in {\mathbb{N}}_0$$
700	699	a1i	$$⊢\phi \to 7\in {\mathbb{N}}_0$$
701	3 700	expcld	$$⊢\phi \to 3^7\in ℂ$$
702	701 355	mulcld	$$⊢\phi \to 3^7\cdot 2\in ℂ$$
703	698 702 441	adddid	$$⊢\phi \to A^4\left(3^7\cdot 2+3^6\right)=A^4{3}^7\cdot 2+A^4{3}^6$$
704	703	eqcomd	$$⊢\phi \to A^4{3}^7\cdot 2+A^4{3}^6=A^4\left(3^7\cdot 2+3^6\right)$$
705	695 704	eqtrd	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3=A^4\left(3^7\cdot 2+3^6\right)$$
706	705	oveq1d	$$⊢\phi \to A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)=A^4\left(3^7\cdot 2+3^6\right)+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)$$
707	706	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)=A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)$$
708	707	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A^4\left(3^7\cdot 2+3^6\right)+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)\right)$$
709	708	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+\left(A3\cdot 23^3{A}^2{3}^{2}A\cdot 3+A{3^{2}A}^3\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
710	487 709	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
711	380	oveq2d	$$⊢\phi \to 3^3{A}^2{3^{2}A}^2=3^3{A}^2{\left(3^2\right)}^2{A}^2$$
712	711	oveq2d	$$⊢\phi \to 33^3{A}^2{3^{2}A}^2=33^3{A}^2{\left(3^2\right)}^2{A}^2$$
713	712	oveq2d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2=A33^3{A}^2{\left(3^2\right)}^2{A}^2$$
714	713	oveq1d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A33^3{A}^2{\left(3^2\right)}^2{A}^2+A3{3^3{A}^2}^2\cdot 3$$
715	10 387	mulcld	$$⊢\phi \to 3^3{A}^2{\left(3^2\right)}^2{A}^2\in ℂ$$
716	3 715	mulcld	$$⊢\phi \to 33^3{A}^2{\left(3^2\right)}^2{A}^2\in ℂ$$
717	8 716	mulcomd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=33^3{A}^2{\left(3^2\right)}^2{A}^{2}A$$
718	3 715	mulcomd	$$⊢\phi \to 33^3{A}^2{\left(3^2\right)}^2{A}^2=3^3{A}^2{\left(3^2\right)}^2{A}^2\cdot 3$$
719	718	oveq1d	$$⊢\phi \to 33^3{A}^2{\left(3^2\right)}^2{A}^{2}A=3^3{A}^2{\left(3^2\right)}^2{A}^2\cdot 3A$$
720	717 719	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=3^3{A}^2{\left(3^2\right)}^2{A}^2\cdot 3A$$
721	286	oveq1d	$$⊢\phi \to 3^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{3}^3{\left(3^2\right)}^2{A}^2$$
722	721	oveq1d	$$⊢\phi \to 3^3{A}^2{\left(3^2\right)}^2{A}^2\cdot 3=A^2{3}^3{\left(3^2\right)}^2{A}^2\cdot 3$$
723	722	oveq1d	$$⊢\phi \to 3^3{A}^2{\left(3^2\right)}^2{A}^2\cdot 3A=A^2{3}^3{\left(3^2\right)}^2{A}^2\cdot 3A$$
724	720 723	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{3}^3{\left(3^2\right)}^2{A}^2\cdot 3A$$
725	291 387	mulcld	$$⊢\phi \to A^2{3}^3{\left(3^2\right)}^2{A}^2\in ℂ$$
726	725 3 8	mulassd	$$⊢\phi \to A^2{3}^3{\left(3^2\right)}^2{A}^2\cdot 3A=A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A$$
727	724 726	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A$$
728	291 387 295	mulassd	$$⊢\phi \to A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A=A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A$$
729	727 728	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A$$
730	387 295	mulcld	$$⊢\phi \to {\left(3^2\right)}^2{A}^{2}3A\in ℂ$$
731	9 6 730	mulassd	$$⊢\phi \to A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A=A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A$$
732	729 731	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A$$
733	6 730	mulcomd	$$⊢\phi \to 3^3{\left(3^2\right)}^2{A}^{2}3A={\left(3^2\right)}^2{A}^{2}3A{3}^3$$
734	733	oveq2d	$$⊢\phi \to A^2{3}^3{\left(3^2\right)}^2{A}^{2}3A=A^2{\left(3^2\right)}^2{A}^{2}3A{3}^3$$
735	732 734	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{\left(3^2\right)}^2{A}^{2}3A{3}^3$$
736	394	oveq1d	$$⊢\phi \to {\left(3^2\right)}^2{A}^{2}3A=A^2{\left(3^2\right)}^{2}3A$$
737	736	oveq1d	$$⊢\phi \to {\left(3^2\right)}^2{A}^{2}3A{3}^3=A^2{\left(3^2\right)}^{2}3A{3}^3$$
738	737	oveq2d	$$⊢\phi \to A^2{\left(3^2\right)}^2{A}^{2}3A{3}^3=A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3$$
739	735 738	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3$$
740	399 295 6	mulassd	$$⊢\phi \to A^2{\left(3^2\right)}^{2}3A{3}^3=A^2{\left(3^2\right)}^{2}3A{3}^3$$
741	740	oveq2d	$$⊢\phi \to A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3=A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3$$
742	739 741	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3$$
743	295 6	mulcld	$$⊢\phi \to 3A{3}^3\in ℂ$$
744	9 386 743	mulassd	$$⊢\phi \to A^2{\left(3^2\right)}^{2}3A{3}^3=A^2{\left(3^2\right)}^{2}3A{3}^3$$
745	744	oveq2d	$$⊢\phi \to A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3=A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3$$
746	742 745	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3$$
747	386 743	mulcomd	$$⊢\phi \to {\left(3^2\right)}^{2}3A{3}^3=3A{3}^3{\left(3^2\right)}^2$$
748	747	oveq2d	$$⊢\phi \to A^2{\left(3^2\right)}^{2}3A{3}^3=A^{2}3A{3}^3{\left(3^2\right)}^2$$
749	748	oveq2d	$$⊢\phi \to A^2{A}^2{\left(3^2\right)}^{2}3A{3}^3=A^2{A}^{2}3A{3}^3{\left(3^2\right)}^2$$
750	746 749	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{A}^{2}3A{3}^3{\left(3^2\right)}^2$$
751	308	oveq1d	$$⊢\phi \to 3A{3}^3=A\cdot 33^3$$
752	751	oveq1d	$$⊢\phi \to 3A{3}^3{\left(3^2\right)}^2=A\cdot 33^3{\left(3^2\right)}^2$$
753	752	oveq2d	$$⊢\phi \to A^{2}3A{3}^3{\left(3^2\right)}^2=A^{2}A\cdot 33^3{\left(3^2\right)}^2$$
754	753	oveq2d	$$⊢\phi \to A^2{A}^{2}3A{3}^3{\left(3^2\right)}^2=A^2{A}^{2}A\cdot 33^3{\left(3^2\right)}^2$$
755	750 754	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{A}^{2}A\cdot 33^3{\left(3^2\right)}^2$$
756	313 6 386	mulassd	$$⊢\phi \to A\cdot 33^3{\left(3^2\right)}^2=A\cdot 33^3{\left(3^2\right)}^2$$
757	756	oveq2d	$$⊢\phi \to A^{2}A\cdot 33^3{\left(3^2\right)}^2=A^{2}A\cdot 33^3{\left(3^2\right)}^2$$
758	757	oveq2d	$$⊢\phi \to A^2{A}^{2}A\cdot 33^3{\left(3^2\right)}^2=A^2{A}^{2}A\cdot 33^3{\left(3^2\right)}^2$$
759	755 758	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{A}^{2}A\cdot 33^3{\left(3^2\right)}^2$$
760	6 386	mulcld	$$⊢\phi \to 3^3{\left(3^2\right)}^2\in ℂ$$
761	8 3 760	mulassd	$$⊢\phi \to A\cdot 33^3{\left(3^2\right)}^2=A33^3{\left(3^2\right)}^2$$
762	761	oveq2d	$$⊢\phi \to A^{2}A\cdot 33^3{\left(3^2\right)}^2=A^{2}A33^3{\left(3^2\right)}^2$$
763	762	oveq2d	$$⊢\phi \to A^2{A}^{2}A\cdot 33^3{\left(3^2\right)}^2=A^2{A}^{2}A33^3{\left(3^2\right)}^2$$
764	759 763	eqtrd	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2=A^2{A}^{2}A33^3{\left(3^2\right)}^2$$
765	764	oveq1d	$$⊢\phi \to A33^3{A}^2{\left(3^2\right)}^2{A}^2+A3{3^3{A}^2}^2\cdot 3=A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
766	714 765	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
767	3 760	mulcld	$$⊢\phi \to 33^3{\left(3^2\right)}^2\in ℂ$$
768	8 767	mulcld	$$⊢\phi \to A33^3{\left(3^2\right)}^2\in ℂ$$
769	9 9 768	mulassd	$$⊢\phi \to A^2{A}^{2}A33^3{\left(3^2\right)}^2=A^2{A}^{2}A33^3{\left(3^2\right)}^2$$
770	769	oveq1d	$$⊢\phi \to A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3=A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
771	766 770	eqtr4d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
772	9 9	mulcld	$$⊢\phi \to A^2{A}^2\in ℂ$$
773	772 8 767	mulassd	$$⊢\phi \to A^2{A}^{2}A33^3{\left(3^2\right)}^2=A^2{A}^{2}A33^3{\left(3^2\right)}^2$$
774	773	oveq1d	$$⊢\phi \to A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3=A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
775	771 774	eqtr4d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
776	8 29 29	expaddd	$$⊢\phi \to A^{2+2}=A^2{A}^2$$
777	776	oveq1d	$$⊢\phi \to A^{2+2}A=A^2{A}^{2}A$$
778	777	eqcomd	$$⊢\phi \to A^2{A}^{2}A=A^{2+2}A$$
779	8 259	expp1d	$$⊢\phi \to A^{2+2+1}=A^{2+2}A$$
780	778 779	eqtr4d	$$⊢\phi \to A^2{A}^{2}A=A^{2+2+1}$$
781	780	oveq1d	$$⊢\phi \to A^2{A}^{2}A33^3{\left(3^2\right)}^2=A^{2+2+1}33^3{\left(3^2\right)}^2$$
782	781	oveq1d	$$⊢\phi \to A^2{A}^{2}A33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3=A^{2+2+1}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
783	775 782	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^{2+2+1}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
784	266	oveq2d	$$⊢\phi \to A^{2+2+1}=A^{4+1}$$
785	784	oveq1d	$$⊢\phi \to A^{2+2+1}33^3{\left(3^2\right)}^2=A^{4+1}33^3{\left(3^2\right)}^2$$
786	785	oveq1d	$$⊢\phi \to A^{2+2+1}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3=A^{4+1}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
787	783 786	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^{4+1}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
788	271	oveq2d	$$⊢\phi \to A^{4+1}=A^5$$
789	788	oveq1d	$$⊢\phi \to A^{4+1}33^3{\left(3^2\right)}^2=A^{5}33^3{\left(3^2\right)}^2$$
790	789	oveq1d	$$⊢\phi \to A^{4+1}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3=A^{5}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
791	787 790	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^{5}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3$$
792	445	oveq2d	$$⊢\phi \to 3^3{3}^{2\cdot 2}=3^3{\left(3^2\right)}^2$$
793	792	oveq2d	$$⊢\phi \to 33^3{3}^{2\cdot 2}=33^3{\left(3^2\right)}^2$$
794	793	eqcomd	$$⊢\phi \to 33^3{\left(3^2\right)}^2=33^3{3}^{2\cdot 2}$$
795	3 449 5	expaddd	$$⊢\phi \to 3^{3+2\cdot 2}=3^3{3}^{2\cdot 2}$$
796	795	oveq2d	$$⊢\phi \to 33^{3+2\cdot 2}=33^3{3}^{2\cdot 2}$$
797	794 796	eqtr4d	$$⊢\phi \to 33^3{\left(3^2\right)}^2=33^{3+2\cdot 2}$$
798	5 449	nn0addcld	$$⊢\phi \to 3+2\cdot 2\in {\mathbb{N}}_0$$
799	3 798	expcld	$$⊢\phi \to 3^{3+2\cdot 2}\in ℂ$$
800	3 799	mulcomd	$$⊢\phi \to 33^{3+2\cdot 2}=3^{3+2\cdot 2}\cdot 3$$
801	797 800	eqtrd	$$⊢\phi \to 33^3{\left(3^2\right)}^2=3^{3+2\cdot 2}\cdot 3$$
802	3 798	expp1d	$$⊢\phi \to 3^{3+2\cdot 2+1}=3^{3+2\cdot 2}\cdot 3$$
803	801 802	eqtr4d	$$⊢\phi \to 33^3{\left(3^2\right)}^2=3^{3+2\cdot 2+1}$$
804	803	oveq2d	$$⊢\phi \to A^{5}33^3{\left(3^2\right)}^2=A^5{3}^{3+2\cdot 2+1}$$
805	804	oveq1d	$$⊢\phi \to A^{5}33^3{\left(3^2\right)}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{3+2\cdot 2+1}+A3{3^3{A}^2}^2\cdot 3$$
806	791 805	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{3+2\cdot 2+1}+A3{3^3{A}^2}^2\cdot 3$$
807	469	oveq2d	$$⊢\phi \to 3+2\cdot 2=3+4$$
808	807	oveq1d	$$⊢\phi \to 3+2\cdot 2+1=3+4+1$$
809	808	oveq2d	$$⊢\phi \to 3^{3+2\cdot 2+1}=3^{3+4+1}$$
810	809	oveq2d	$$⊢\phi \to A^5{3}^{3+2\cdot 2+1}=A^5{3}^{3+4+1}$$
811	810	oveq1d	$$⊢\phi \to A^5{3}^{3+2\cdot 2+1}+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{3+4+1}+A3{3^3{A}^2}^2\cdot 3$$
812	806 811	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{3+4+1}+A3{3^3{A}^2}^2\cdot 3$$
813	586	oveq2d	$$⊢\phi \to 3+3+1=3+4$$
814	813	oveq1d	$$⊢\phi \to 3+\left(3+1\right)+1=3+4+1$$
815	814	oveq2d	$$⊢\phi \to 3^{3+\left(3+1\right)+1}=3^{3+4+1}$$
816	815	oveq2d	$$⊢\phi \to A^5{3}^{3+\left(3+1\right)+1}=A^5{3}^{3+4+1}$$
817	816	oveq1d	$$⊢\phi \to A^5{3}^{3+\left(3+1\right)+1}+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{3+4+1}+A3{3^3{A}^2}^2\cdot 3$$
818	812 817	eqtr4d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{3+\left(3+1\right)+1}+A3{3^3{A}^2}^2\cdot 3$$
819	3 3 357	addassd	$$⊢\phi \to 3+3+1=3+3+1$$
820	819	oveq1d	$$⊢\phi \to \left(3+3\right)+1+1=3+\left(3+1\right)+1$$
821	820	oveq2d	$$⊢\phi \to 3^{\left(3+3\right)+1+1}=3^{3+\left(3+1\right)+1}$$
822	821	oveq2d	$$⊢\phi \to A^5{3}^{\left(3+3\right)+1+1}=A^5{3}^{3+\left(3+1\right)+1}$$
823	822	oveq1d	$$⊢\phi \to A^5{3}^{\left(3+3\right)+1+1}+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{3+\left(3+1\right)+1}+A3{3^3{A}^2}^2\cdot 3$$
824	818 823	eqtr4d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{\left(3+3\right)+1+1}+A3{3^3{A}^2}^2\cdot 3$$
825		3p3e6	$$⊢3+3=6$$
826	825	a1i	$$⊢\phi \to 3+3=6$$
827	826	oveq1d	$$⊢\phi \to 3+3+1=6+1$$
828	827	oveq1d	$$⊢\phi \to \left(3+3\right)+1+1=6+1+1$$
829	828	oveq2d	$$⊢\phi \to 3^{\left(3+3\right)+1+1}=3^{6+1+1}$$
830	829	oveq2d	$$⊢\phi \to A^5{3}^{\left(3+3\right)+1+1}=A^5{3}^{6+1+1}$$
831	830	oveq1d	$$⊢\phi \to A^5{3}^{\left(3+3\right)+1+1}+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{6+1+1}+A3{3^3{A}^2}^2\cdot 3$$
832	824 831	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{6+1+1}+A3{3^3{A}^2}^2\cdot 3$$
833	649	oveq1d	$$⊢\phi \to 6+1+1=7+1$$
834	833	oveq2d	$$⊢\phi \to 3^{6+1+1}=3^{7+1}$$
835	834	oveq2d	$$⊢\phi \to A^5{3}^{6+1+1}=A^5{3}^{7+1}$$
836	835	oveq1d	$$⊢\phi \to A^5{3}^{6+1+1}+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{7+1}+A3{3^3{A}^2}^2\cdot 3$$
837	832 836	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^{7+1}+A3{3^3{A}^2}^2\cdot 3$$
838		7p1e8	$$⊢7+1=8$$
839	838	a1i	$$⊢\phi \to 7+1=8$$
840	839	oveq2d	$$⊢\phi \to 3^{7+1}=3^8$$
841	840	oveq2d	$$⊢\phi \to A^5{3}^{7+1}=A^5{3}^8$$
842	841	oveq1d	$$⊢\phi \to A^5{3}^{7+1}+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A3{3^3{A}^2}^2\cdot 3$$
843	837 842	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A3{3^3{A}^2}^2\cdot 3$$
844	6 9 29	mulexpd	$$⊢\phi \to {3^3{A}^2}^2={\left(3^3\right)}^2{\left(A^2\right)}^2$$
845	844	oveq1d	$$⊢\phi \to {3^3{A}^2}^2\cdot 3={\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
846	845	oveq2d	$$⊢\phi \to 3{3^3{A}^2}^2\cdot 3=3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
847	846	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2\cdot 3=A3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
848	847	oveq2d	$$⊢\phi \to A^5{3}^8+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
849	843 848	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
850	3 29 5	expmuld	$$⊢\phi \to 3^{3\cdot 2}={\left(3^3\right)}^2$$
851	850	oveq1d	$$⊢\phi \to 3^{3\cdot 2}{\left(A^2\right)}^2={\left(3^3\right)}^2{\left(A^2\right)}^2$$
852	851	oveq1d	$$⊢\phi \to 3^{3\cdot 2}{\left(A^2\right)}^2\cdot 3={\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
853	852	oveq2d	$$⊢\phi \to 33^{3\cdot 2}{\left(A^2\right)}^2\cdot 3=3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
854	853	oveq2d	$$⊢\phi \to A33^{3\cdot 2}{\left(A^2\right)}^2\cdot 3=A3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3$$
855	854	eqcomd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3=A33^{3\cdot 2}{\left(A^2\right)}^2\cdot 3$$
856	8 29 29	expmuld	$$⊢\phi \to A^{2\cdot 2}={\left(A^2\right)}^2$$
857	856	oveq2d	$$⊢\phi \to 3^{3\cdot 2}{A}^{2\cdot 2}=3^{3\cdot 2}{\left(A^2\right)}^2$$
858	857	oveq1d	$$⊢\phi \to 3^{3\cdot 2}{A}^{2\cdot 2}\cdot 3=3^{3\cdot 2}{\left(A^2\right)}^2\cdot 3$$
859	858	oveq2d	$$⊢\phi \to 33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3=33^{3\cdot 2}{\left(A^2\right)}^2\cdot 3$$
860	859	oveq2d	$$⊢\phi \to A33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3=A33^{3\cdot 2}{\left(A^2\right)}^2\cdot 3$$
861	855 860	eqtr4d	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3=A33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3$$
862	861	oveq2d	$$⊢\phi \to A^5{3}^8+A3{\left(3^3\right)}^2{\left(A^2\right)}^2\cdot 3=A^5{3}^8+A33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3$$
863	849 862	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3$$
864	689	a1i	$$⊢\phi \to 3\cdot 2=6$$
865	864	oveq2d	$$⊢\phi \to 3^{3\cdot 2}=3^6$$
866	865	oveq1d	$$⊢\phi \to 3^{3\cdot 2}{A}^{2\cdot 2}=3^6{A}^{2\cdot 2}$$
867	866	oveq1d	$$⊢\phi \to 3^{3\cdot 2}{A}^{2\cdot 2}\cdot 3=3^6{A}^{2\cdot 2}\cdot 3$$
868	867	oveq2d	$$⊢\phi \to 33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3=33^6{A}^{2\cdot 2}\cdot 3$$
869	868	oveq2d	$$⊢\phi \to A33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3=A33^6{A}^{2\cdot 2}\cdot 3$$
870	869	oveq2d	$$⊢\phi \to A^5{3}^8+A33^{3\cdot 2}{A}^{2\cdot 2}\cdot 3=A^5{3}^8+A33^6{A}^{2\cdot 2}\cdot 3$$
871	863 870	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A33^6{A}^{2\cdot 2}\cdot 3$$
872	469	oveq2d	$$⊢\phi \to A^{2\cdot 2}=A^4$$
873	872	oveq2d	$$⊢\phi \to 3^6{A}^{2\cdot 2}=3^6{A}^4$$
874	873	oveq1d	$$⊢\phi \to 3^6{A}^{2\cdot 2}\cdot 3=3^6{A}^4\cdot 3$$
875	874	oveq2d	$$⊢\phi \to 33^6{A}^{2\cdot 2}\cdot 3=33^6{A}^4\cdot 3$$
876	875	oveq2d	$$⊢\phi \to A33^6{A}^{2\cdot 2}\cdot 3=A33^6{A}^4\cdot 3$$
877	876	oveq2d	$$⊢\phi \to A^5{3}^8+A33^6{A}^{2\cdot 2}\cdot 3=A^5{3}^8+A33^6{A}^4\cdot 3$$
878	871 877	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A33^6{A}^4\cdot 3$$
879	441 698	mulcld	$$⊢\phi \to 3^6{A}^4\in ℂ$$
880	879 3	mulcld	$$⊢\phi \to 3^6{A}^4\cdot 3\in ℂ$$
881	3 880	mulcld	$$⊢\phi \to 33^6{A}^4\cdot 3\in ℂ$$
882	8 881	mulcomd	$$⊢\phi \to A33^6{A}^4\cdot 3=33^6{A}^4\cdot 3A$$
883	3 880	mulcomd	$$⊢\phi \to 33^6{A}^4\cdot 3=3^6{A}^4\cdot 3\cdot 3$$
884	883	oveq1d	$$⊢\phi \to 33^6{A}^4\cdot 3A=3^6{A}^4\cdot 3\cdot 3A$$
885	882 884	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=3^6{A}^4\cdot 3\cdot 3A$$
886	441 698	mulcomd	$$⊢\phi \to 3^6{A}^4=A^4{3}^6$$
887	886	oveq1d	$$⊢\phi \to 3^6{A}^4\cdot 3=A^4{3}^6\cdot 3$$
888	887	oveq1d	$$⊢\phi \to 3^6{A}^4\cdot 3\cdot 3=A^4{3}^6\cdot 3\cdot 3$$
889	888	oveq1d	$$⊢\phi \to 3^6{A}^4\cdot 3\cdot 3A=A^4{3}^6\cdot 3\cdot 3A$$
890	885 889	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^4{3}^6\cdot 3\cdot 3A$$
891	698 441	mulcld	$$⊢\phi \to A^4{3}^6\in ℂ$$
892	891 3	mulcld	$$⊢\phi \to A^4{3}^6\cdot 3\in ℂ$$
893	892 3 8	mulassd	$$⊢\phi \to A^4{3}^6\cdot 3\cdot 3A=A^4{3}^6\cdot 33A$$
894	890 893	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^4{3}^6\cdot 33A$$
895	891 3 295	mulassd	$$⊢\phi \to A^4{3}^6\cdot 33A=A^4{3}^{6}33A$$
896	894 895	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^4{3}^{6}33A$$
897	698 441 405	mulassd	$$⊢\phi \to A^4{3}^{6}33A=A^4{3}^{6}33A$$
898	896 897	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^4{3}^{6}33A$$
899	441 405	mulcomd	$$⊢\phi \to 3^{6}33A=33A{3}^6$$
900	899	oveq2d	$$⊢\phi \to A^4{3}^{6}33A=A^{4}33A{3}^6$$
901	898 900	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^{4}33A{3}^6$$
902	411	oveq1d	$$⊢\phi \to 33A{3}^6=3A\cdot 33^6$$
903	902	oveq2d	$$⊢\phi \to A^{4}33A{3}^6=A^{4}3A\cdot 33^6$$
904	901 903	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^{4}3A\cdot 33^6$$
905	415	oveq1d	$$⊢\phi \to 3A\cdot 33^6=A\cdot 3\cdot 33^6$$
906	905	oveq2d	$$⊢\phi \to A^{4}3A\cdot 33^6=A^{4}A\cdot 3\cdot 33^6$$
907	904 906	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^{4}A\cdot 3\cdot 33^6$$
908	313 3 441	mulassd	$$⊢\phi \to A\cdot 3\cdot 33^6=A\cdot 333^6$$
909	908	oveq2d	$$⊢\phi \to A^{4}A\cdot 3\cdot 33^6=A^{4}A\cdot 333^6$$
910	907 909	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^{4}A\cdot 333^6$$
911	3 441	mulcld	$$⊢\phi \to 33^6\in ℂ$$
912	8 3 911	mulassd	$$⊢\phi \to A\cdot 333^6=A333^6$$
913	912	oveq2d	$$⊢\phi \to A^{4}A\cdot 333^6=A^{4}A333^6$$
914	910 913	eqtrd	$$⊢\phi \to A33^6{A}^4\cdot 3=A^{4}A333^6$$
915	914	oveq2d	$$⊢\phi \to A^5{3}^8+A33^6{A}^4\cdot 3=A^5{3}^8+A^{4}A333^6$$
916	878 915	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A^{4}A333^6$$
917	3 911	mulcld	$$⊢\phi \to 333^6\in ℂ$$
918	698 8 917	mulassd	$$⊢\phi \to A^{4}A333^6=A^{4}A333^6$$
919	918	oveq2d	$$⊢\phi \to A^5{3}^8+A^{4}A333^6=A^5{3}^8+A^{4}A333^6$$
920	916 919	eqtr4d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A^{4}A333^6$$
921	8 697	expp1d	$$⊢\phi \to A^{4+1}=A^{4}A$$
922	921	eqcomd	$$⊢\phi \to A^{4}A=A^{4+1}$$
923	922	oveq1d	$$⊢\phi \to A^{4}A333^6=A^{4+1}333^6$$
924	923	oveq2d	$$⊢\phi \to A^5{3}^8+A^{4}A333^6=A^5{3}^8+A^{4+1}333^6$$
925	920 924	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A^{4+1}333^6$$
926	788	oveq1d	$$⊢\phi \to A^{4+1}333^6=A^{5}333^6$$
927	926	oveq2d	$$⊢\phi \to A^5{3}^8+A^{4+1}333^6=A^5{3}^8+A^{5}333^6$$
928	925 927	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A^{5}333^6$$
929	3 441	mulcomd	$$⊢\phi \to 33^6=3^6\cdot 3$$
930	929	oveq2d	$$⊢\phi \to 333^6=33^6\cdot 3$$
931	3 440	expp1d	$$⊢\phi \to 3^{6+1}=3^6\cdot 3$$
932	931	oveq2d	$$⊢\phi \to 33^{6+1}=33^6\cdot 3$$
933	930 932	eqtr4d	$$⊢\phi \to 333^6=33^{6+1}$$
934	440 458	nn0addcld	$$⊢\phi \to 6+1\in {\mathbb{N}}_0$$
935	3 934	expcld	$$⊢\phi \to 3^{6+1}\in ℂ$$
936	3 935	mulcomd	$$⊢\phi \to 33^{6+1}=3^{6+1}\cdot 3$$
937	933 936	eqtrd	$$⊢\phi \to 333^6=3^{6+1}\cdot 3$$
938	3 934	expp1d	$$⊢\phi \to 3^{6+1+1}=3^{6+1}\cdot 3$$
939	937 938	eqtr4d	$$⊢\phi \to 333^6=3^{6+1+1}$$
940	939	oveq2d	$$⊢\phi \to A^{5}333^6=A^5{3}^{6+1+1}$$
941	940	oveq2d	$$⊢\phi \to A^5{3}^8+A^{5}333^6=A^5{3}^8+A^5{3}^{6+1+1}$$
942	928 941	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A^5{3}^{6+1+1}$$
943	835	oveq2d	$$⊢\phi \to A^5{3}^8+A^5{3}^{6+1+1}=A^5{3}^8+A^5{3}^{7+1}$$
944	942 943	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A^5{3}^{7+1}$$
945	841	oveq2d	$$⊢\phi \to A^5{3}^8+A^5{3}^{7+1}=A^5{3}^8+A^5{3}^8$$
946	944 945	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5{3}^8+A^5{3}^8$$
947	8 609	expcld	$$⊢\phi \to A^5\in ℂ$$
948		8nn0	$$⊢8\in {\mathbb{N}}_0$$
949	948	a1i	$$⊢\phi \to 8\in {\mathbb{N}}_0$$
950	3 949	expcld	$$⊢\phi \to 3^8\in ℂ$$
951	947 950 950	adddid	$$⊢\phi \to A^5\left(3^8+3^8\right)=A^5{3}^8+A^5{3}^8$$
952	951	eqcomd	$$⊢\phi \to A^5{3}^8+A^5{3}^8=A^5\left(3^8+3^8\right)$$
953	946 952	eqtrd	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3=A^5\left(3^8+3^8\right)$$
954	953	oveq1d	$$⊢\phi \to A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)=A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)$$
955	954	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3\right)+\left(A^4\left(3^7\cdot 2+3^6\right)+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)\right)=A3{3^3{A}^2}^2{3}^{2}A+A^5\left(3^8+3^8\right)+\left(A^4\left(3^7\cdot 2+3^6\right)+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)\right)$$
956	955	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A33^3{A}^2{3^{2}A}^2+A3{3^3{A}^2}^2\cdot 3+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
957	710 956	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
958	844	oveq1d	$$⊢\phi \to {3^3{A}^2}^2{3}^{2}A={\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A$$
959	958	oveq2d	$$⊢\phi \to 3{3^3{A}^2}^2{3}^{2}A=3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A$$
960	959	oveq2d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A$$
961	6	sqcld	$$⊢\phi \to {\left(3^3\right)}^2\in ℂ$$
962	9	sqcld	$$⊢\phi \to {\left(A^2\right)}^2\in ℂ$$
963	961 962	mulcld	$$⊢\phi \to {\left(3^3\right)}^2{\left(A^2\right)}^2\in ℂ$$
964	963 12	mulcld	$$⊢\phi \to {\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A\in ℂ$$
965	3 964	mulcld	$$⊢\phi \to 3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A\in ℂ$$
966	8 965	mulcomd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A=3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}AA$$
967	3 964	mulcomd	$$⊢\phi \to 3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A\cdot 3$$
968	967	oveq1d	$$⊢\phi \to 3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}AA={\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A\cdot 3A$$
969	966 968	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A\cdot 3A$$
970	961 962	mulcomd	$$⊢\phi \to {\left(3^3\right)}^2{\left(A^2\right)}^2={\left(A^2\right)}^2{\left(3^3\right)}^2$$
971	970	oveq1d	$$⊢\phi \to {\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A$$
972	971	oveq1d	$$⊢\phi \to {\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A\cdot 3={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A\cdot 3$$
973	972	oveq1d	$$⊢\phi \to {\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A\cdot 3A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A\cdot 3A$$
974	969 973	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A\cdot 3A$$
975	962 961	mulcld	$$⊢\phi \to {\left(A^2\right)}^2{\left(3^3\right)}^2\in ℂ$$
976	975 12	mulcld	$$⊢\phi \to {\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A\in ℂ$$
977	976 3 8	mulassd	$$⊢\phi \to {\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A\cdot 3A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A$$
978	974 977	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A$$
979	975 12 295	mulassd	$$⊢\phi \to {\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A$$
980	978 979	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A$$
981	12 295	mulcld	$$⊢\phi \to 3^{2}A3A\in ℂ$$
982	962 961 981	mulassd	$$⊢\phi \to {\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A$$
983	980 982	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A$$
984	961 981	mulcomd	$$⊢\phi \to {\left(3^3\right)}^2{3}^{2}A3A=3^{2}A3A{\left(3^3\right)}^2$$
985	984	oveq2d	$$⊢\phi \to {\left(A^2\right)}^2{\left(3^3\right)}^2{3}^{2}A3A={\left(A^2\right)}^2{3}^{2}A3A{\left(3^3\right)}^2$$
986	983 985	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^2{3}^{2}A3A{\left(3^3\right)}^2$$
987	232	oveq1d	$$⊢\phi \to 3^{2}A3A=A{3}^{2}3A$$
988	987	oveq1d	$$⊢\phi \to 3^{2}A3A{\left(3^3\right)}^2=A{3}^{2}3A{\left(3^3\right)}^2$$
989	988	oveq2d	$$⊢\phi \to {\left(A^2\right)}^2{3}^{2}A3A{\left(3^3\right)}^2={\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2$$
990	986 989	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2$$
991	237 295 961	mulassd	$$⊢\phi \to A{3}^{2}3A{\left(3^3\right)}^2=A{3}^{2}3A{\left(3^3\right)}^2$$
992	991	oveq2d	$$⊢\phi \to {\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2={\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2$$
993	990 992	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2$$
994	295 961	mulcld	$$⊢\phi \to 3A{\left(3^3\right)}^2\in ℂ$$
995	8 11 994	mulassd	$$⊢\phi \to A{3}^{2}3A{\left(3^3\right)}^2=A{3}^{2}3A{\left(3^3\right)}^2$$
996	995	oveq2d	$$⊢\phi \to {\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2={\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2$$
997	993 996	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2$$
998	11 994	mulcomd	$$⊢\phi \to 3^{2}3A{\left(3^3\right)}^2=3A{\left(3^3\right)}^2{3}^2$$
999	998	oveq2d	$$⊢\phi \to A{3}^{2}3A{\left(3^3\right)}^2=A3A{\left(3^3\right)}^2{3}^2$$
1000	999	oveq2d	$$⊢\phi \to {\left(A^2\right)}^{2}A{3}^{2}3A{\left(3^3\right)}^2={\left(A^2\right)}^{2}A3A{\left(3^3\right)}^2{3}^2$$
1001	997 1000	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^{2}A3A{\left(3^3\right)}^2{3}^2$$
1002	308	oveq1d	$$⊢\phi \to 3A{\left(3^3\right)}^2=A\cdot 3{\left(3^3\right)}^2$$
1003	1002	oveq1d	$$⊢\phi \to 3A{\left(3^3\right)}^2{3}^2=A\cdot 3{\left(3^3\right)}^2{3}^2$$
1004	1003	oveq2d	$$⊢\phi \to A3A{\left(3^3\right)}^2{3}^2=AA\cdot 3{\left(3^3\right)}^2{3}^2$$
1005	1004	oveq2d	$$⊢\phi \to {\left(A^2\right)}^{2}A3A{\left(3^3\right)}^2{3}^2={\left(A^2\right)}^{2}AA\cdot 3{\left(3^3\right)}^2{3}^2$$
1006	1001 1005	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^{2}AA\cdot 3{\left(3^3\right)}^2{3}^2$$
1007	313 961 11	mulassd	$$⊢\phi \to A\cdot 3{\left(3^3\right)}^2{3}^2=A\cdot 3{\left(3^3\right)}^2{3}^2$$
1008	1007	oveq2d	$$⊢\phi \to AA\cdot 3{\left(3^3\right)}^2{3}^2=AA\cdot 3{\left(3^3\right)}^2{3}^2$$
1009	1008	oveq2d	$$⊢\phi \to {\left(A^2\right)}^{2}AA\cdot 3{\left(3^3\right)}^2{3}^2={\left(A^2\right)}^{2}AA\cdot 3{\left(3^3\right)}^2{3}^2$$
1010	1006 1009	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^{2}AA\cdot 3{\left(3^3\right)}^2{3}^2$$
1011	961 11	mulcld	$$⊢\phi \to {\left(3^3\right)}^2{3}^2\in ℂ$$
1012	8 3 1011	mulassd	$$⊢\phi \to A\cdot 3{\left(3^3\right)}^2{3}^2=A3{\left(3^3\right)}^2{3}^2$$
1013	1012	oveq2d	$$⊢\phi \to AA\cdot 3{\left(3^3\right)}^2{3}^2=AA3{\left(3^3\right)}^2{3}^2$$
1014	1013	oveq2d	$$⊢\phi \to {\left(A^2\right)}^{2}AA\cdot 3{\left(3^3\right)}^2{3}^2={\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2$$
1015	1010 1014	eqtrd	$$⊢\phi \to A3{\left(3^3\right)}^2{\left(A^2\right)}^2{3}^{2}A={\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2$$
1016	960 1015	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A={\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2$$
1017	3 1011	mulcld	$$⊢\phi \to 3{\left(3^3\right)}^2{3}^2\in ℂ$$
1018	8 1017	mulcld	$$⊢\phi \to A3{\left(3^3\right)}^2{3}^2\in ℂ$$
1019	962 8 1018	mulassd	$$⊢\phi \to {\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2={\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2$$
1020	1016 1019	eqtr4d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A={\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2$$
1021	962 8	mulcld	$$⊢\phi \to {\left(A^2\right)}^{2}A\in ℂ$$
1022	1021 8 1017	mulassd	$$⊢\phi \to {\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2={\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2$$
1023	1020 1022	eqtr4d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A={\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2$$
1024	856	oveq1d	$$⊢\phi \to A^{2\cdot 2}A={\left(A^2\right)}^{2}A$$
1025	1024	oveq1d	$$⊢\phi \to A^{2\cdot 2}AA={\left(A^2\right)}^{2}AA$$
1026	1025	eqcomd	$$⊢\phi \to {\left(A^2\right)}^{2}AA=A^{2\cdot 2}AA$$
1027	8 449	expp1d	$$⊢\phi \to A^{2\cdot 2+1}=A^{2\cdot 2}A$$
1028	1027	oveq1d	$$⊢\phi \to A^{2\cdot 2+1}A=A^{2\cdot 2}AA$$
1029	1026 1028	eqtr4d	$$⊢\phi \to {\left(A^2\right)}^{2}AA=A^{2\cdot 2+1}A$$
1030	8 459	expp1d	$$⊢\phi \to A^{2\cdot 2+1+1}=A^{2\cdot 2+1}A$$
1031	1029 1030	eqtr4d	$$⊢\phi \to {\left(A^2\right)}^{2}AA=A^{2\cdot 2+1+1}$$
1032	1031	oveq1d	$$⊢\phi \to {\left(A^2\right)}^{2}AA3{\left(3^3\right)}^2{3}^2=A^{2\cdot 2+1+1}3{\left(3^3\right)}^2{3}^2$$
1033	1023 1032	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^{2\cdot 2+1+1}3{\left(3^3\right)}^2{3}^2$$
1034	471	oveq2d	$$⊢\phi \to A^{2\cdot 2+1+1}=A^{4+1+1}$$
1035	1034	oveq1d	$$⊢\phi \to A^{2\cdot 2+1+1}3{\left(3^3\right)}^2{3}^2=A^{4+1+1}3{\left(3^3\right)}^2{3}^2$$
1036	1033 1035	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^{4+1+1}3{\left(3^3\right)}^2{3}^2$$
1037	369	oveq2d	$$⊢\phi \to A^{4+1+1}=A^{5+1}$$
1038	1037	oveq1d	$$⊢\phi \to A^{4+1+1}3{\left(3^3\right)}^2{3}^2=A^{5+1}3{\left(3^3\right)}^2{3}^2$$
1039	1036 1038	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^{5+1}3{\left(3^3\right)}^2{3}^2$$
1040	375	oveq2d	$$⊢\phi \to A^{5+1}=A^6$$
1041	1040	oveq1d	$$⊢\phi \to A^{5+1}3{\left(3^3\right)}^2{3}^2=A^{6}3{\left(3^3\right)}^2{3}^2$$
1042	1039 1041	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^{6}3{\left(3^3\right)}^2{3}^2$$
1043	850	oveq1d	$$⊢\phi \to 3^{3\cdot 2}{3}^2={\left(3^3\right)}^2{3}^2$$
1044	1043	oveq2d	$$⊢\phi \to 33^{3\cdot 2}{3}^2=3{\left(3^3\right)}^2{3}^2$$
1045	1044	eqcomd	$$⊢\phi \to 3{\left(3^3\right)}^2{3}^2=33^{3\cdot 2}{3}^2$$
1046	3 29 30	expaddd	$$⊢\phi \to 3^{3\cdot 2+2}=3^{3\cdot 2}{3}^2$$
1047	1046	oveq2d	$$⊢\phi \to 33^{3\cdot 2+2}=33^{3\cdot 2}{3}^2$$
1048	1045 1047	eqtr4d	$$⊢\phi \to 3{\left(3^3\right)}^2{3}^2=33^{3\cdot 2+2}$$
1049	30 29	nn0addcld	$$⊢\phi \to 3\cdot 2+2\in {\mathbb{N}}_0$$
1050	3 1049	expcld	$$⊢\phi \to 3^{3\cdot 2+2}\in ℂ$$
1051	3 1050	mulcomd	$$⊢\phi \to 33^{3\cdot 2+2}=3^{3\cdot 2+2}\cdot 3$$
1052	1048 1051	eqtrd	$$⊢\phi \to 3{\left(3^3\right)}^2{3}^2=3^{3\cdot 2+2}\cdot 3$$
1053	3 1049	expp1d	$$⊢\phi \to 3^{3\cdot 2+2+1}=3^{3\cdot 2+2}\cdot 3$$
1054	1052 1053	eqtr4d	$$⊢\phi \to 3{\left(3^3\right)}^2{3}^2=3^{3\cdot 2+2+1}$$
1055	1054	oveq2d	$$⊢\phi \to A^{6}3{\left(3^3\right)}^2{3}^2=A^6{3}^{3\cdot 2+2+1}$$
1056	1042 1055	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^6{3}^{3\cdot 2+2+1}$$
1057	864	oveq1d	$$⊢\phi \to 3\cdot 2+2=6+2$$
1058	1057	oveq1d	$$⊢\phi \to 3\cdot 2+2+1=6+2+1$$
1059	1058	oveq2d	$$⊢\phi \to 3^{3\cdot 2+2+1}=3^{6+2+1}$$
1060	1059	oveq2d	$$⊢\phi \to A^6{3}^{3\cdot 2+2+1}=A^6{3}^{6+2+1}$$
1061	1056 1060	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^6{3}^{6+2+1}$$
1062		6p2e8	$$⊢6+2=8$$
1063	1062	a1i	$$⊢\phi \to 6+2=8$$
1064	1063	oveq1d	$$⊢\phi \to 6+2+1=8+1$$
1065	1064	oveq2d	$$⊢\phi \to 3^{6+2+1}=3^{8+1}$$
1066	1065	oveq2d	$$⊢\phi \to A^6{3}^{6+2+1}=A^6{3}^{8+1}$$
1067	1061 1066	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^6{3}^{8+1}$$
1068		8p1e9	$$⊢8+1=9$$
1069	1068	a1i	$$⊢\phi \to 8+1=9$$
1070	1069	oveq2d	$$⊢\phi \to 3^{8+1}=3^9$$
1071	1070	oveq2d	$$⊢\phi \to A^6{3}^{8+1}=A^6{3}^9$$
1072	1067 1071	eqtrd	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A=A^6{3}^9$$
1073	1072	oveq1d	$$⊢\phi \to A3{3^3{A}^2}^2{3}^{2}A+A^5\left(3^8+3^8\right)+\left(A^4\left(3^7\cdot 2+3^6\right)+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)\right)=A^6{3}^9+A^5\left(3^8+3^8\right)+\left(A^4\left(3^7\cdot 2+3^6\right)+A^3\left(3^6+3^6\right)+\left(A^2{3}^5+A{3}^3\right)\right)$$
1074	1073	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3+A3{3^3{A}^2}^2{3}^{2}A+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)=A{3^3{A}^2}^3+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
1075	957 1074	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A{3^3{A}^2}^3+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
1076	6 9 5	mulexpd	$$⊢\phi \to {3^3{A}^2}^3={\left(3^3\right)}^3{\left(A^2\right)}^3$$
1077	1076	oveq2d	$$⊢\phi \to A{3^3{A}^2}^3=A{\left(3^3\right)}^3{\left(A^2\right)}^3$$
1078	6 5	expcld	$$⊢\phi \to {\left(3^3\right)}^3\in ℂ$$
1079	9 5	expcld	$$⊢\phi \to {\left(A^2\right)}^3\in ℂ$$
1080	1078 1079	mulcomd	$$⊢\phi \to {\left(3^3\right)}^3{\left(A^2\right)}^3={\left(A^2\right)}^3{\left(3^3\right)}^3$$
1081	1080	oveq2d	$$⊢\phi \to A{\left(3^3\right)}^3{\left(A^2\right)}^3=A{\left(A^2\right)}^3{\left(3^3\right)}^3$$
1082	1077 1081	eqtrd	$$⊢\phi \to A{3^3{A}^2}^3=A{\left(A^2\right)}^3{\left(3^3\right)}^3$$
1083	8 1079 1078	mulassd	$$⊢\phi \to A{\left(A^2\right)}^3{\left(3^3\right)}^3=A{\left(A^2\right)}^3{\left(3^3\right)}^3$$
1084	1082 1083	eqtr4d	$$⊢\phi \to A{3^3{A}^2}^3=A{\left(A^2\right)}^3{\left(3^3\right)}^3$$
1085	8 5 29	expmuld	$$⊢\phi \to A^{2\cdot 3}={\left(A^2\right)}^3$$
1086	1085	oveq2d	$$⊢\phi \to A{A}^{2\cdot 3}=A{\left(A^2\right)}^3$$
1087	1086	eqcomd	$$⊢\phi \to A{\left(A^2\right)}^3=A{A}^{2\cdot 3}$$
1088	29 5	nn0mulcld	$$⊢\phi \to 2\cdot 3\in {\mathbb{N}}_0$$
1089	8 1088	expcld	$$⊢\phi \to A^{2\cdot 3}\in ℂ$$
1090	8 1089	mulcomd	$$⊢\phi \to A{A}^{2\cdot 3}=A^{2\cdot 3}A$$
1091	1087 1090	eqtrd	$$⊢\phi \to A{\left(A^2\right)}^3=A^{2\cdot 3}A$$
1092	8 1088	expp1d	$$⊢\phi \to A^{2\cdot 3+1}=A^{2\cdot 3}A$$
1093	1091 1092	eqtr4d	$$⊢\phi \to A{\left(A^2\right)}^3=A^{2\cdot 3+1}$$
1094	1093	oveq1d	$$⊢\phi \to A{\left(A^2\right)}^3{\left(3^3\right)}^3=A^{2\cdot 3+1}{\left(3^3\right)}^3$$
1095	1084 1094	eqtrd	$$⊢\phi \to A{3^3{A}^2}^3=A^{2\cdot 3+1}{\left(3^3\right)}^3$$
1096	691	oveq1d	$$⊢\phi \to 2\cdot 3+1=6+1$$
1097	1096	oveq2d	$$⊢\phi \to A^{2\cdot 3+1}=A^{6+1}$$
1098	1097	oveq1d	$$⊢\phi \to A^{2\cdot 3+1}{\left(3^3\right)}^3=A^{6+1}{\left(3^3\right)}^3$$
1099	1095 1098	eqtrd	$$⊢\phi \to A{3^3{A}^2}^3=A^{6+1}{\left(3^3\right)}^3$$
1100	649	oveq2d	$$⊢\phi \to A^{6+1}=A^7$$
1101	1100	oveq1d	$$⊢\phi \to A^{6+1}{\left(3^3\right)}^3=A^7{\left(3^3\right)}^3$$
1102	1099 1101	eqtrd	$$⊢\phi \to A{3^3{A}^2}^3=A^7{\left(3^3\right)}^3$$
1103	1102	oveq1d	$$⊢\phi \to A{3^3{A}^2}^3+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)=A^7{\left(3^3\right)}^3+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
1104	1075 1103	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A^7{\left(3^3\right)}^3+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
1105	3 5 5	expmuld	$$⊢\phi \to 3^{3\cdot 3}={\left(3^3\right)}^3$$
1106	1105	eqcomd	$$⊢\phi \to {\left(3^3\right)}^3=3^{3\cdot 3}$$
1107	1106	oveq2d	$$⊢\phi \to A^7{\left(3^3\right)}^3=A^7{3}^{3\cdot 3}$$
1108	1107	oveq1d	$$⊢\phi \to A^7{\left(3^3\right)}^3+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)=A^7{3}^{3\cdot 3}+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
1109	1104 1108	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A^7{3}^{3\cdot 3}+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
1110		3t3e9	$$⊢3\cdot 3=9$$
1111	1110	a1i	$$⊢\phi \to 3\cdot 3=9$$
1112	1111	oveq2d	$$⊢\phi \to 3^{3\cdot 3}=3^9$$
1113	1112	oveq2d	$$⊢\phi \to A^7{3}^{3\cdot 3}=A^7{3}^9$$
1114	1113	oveq1d	$$⊢\phi \to A^7{3}^{3\cdot 3}+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)=A^7{3}^9+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$
1115	1109 1114	eqtrd	$$⊢\phi \to A{\left(3^3{A}^2+3^{2}A+3\right)}^3=A^7{3}^9+A^6{3}^9+\left(A^5\left(3^8+3^8\right)+A^4\left(3^7\cdot 2+3^6\right)+\left(A^3\left(3^6+3^6\right)+A^2{3}^5+A{3}^3\right)\right)$$