Theorem 2lgsoddprmlem3b

Description: Lemma 2 for 2lgsoddprmlem3 . (Contributed by AV, 20-Jul-2021)

	Ref	Expression
Assertion	2lgsoddprmlem3b	$$⊢\frac{3^2-1}{8}=1$$

Proof

Step	Hyp	Ref	Expression
1		sq3	$$⊢3^2=9$$
2	1	oveq1i	$$⊢3^2-1=9-1$$
3		9m1e8	$$⊢9-1=8$$
4	2 3	eqtri	$$⊢3^2-1=8$$
5	4	oveq1i	$$⊢\frac{3^2-1}{8}=\frac{8}{8}$$
6		8cn	$$⊢8\in ℂ$$
7		0re	$$⊢0\in ℝ$$
8		8pos	$$⊢0<8$$
9	7 8	gtneii	$$⊢8\ne 0$$
10	6 9	dividi	$$⊢\frac{8}{8}=1$$
11	5 10	eqtri	$$⊢\frac{3^2-1}{8}=1$$