Metamath Proof Explorer


Theorem fmtno5faclem3

Description: Lemma 3 for fmtno5fac . (Contributed by AV, 22-Jul-2021)

Ref Expression
Assertion fmtno5faclem3 ⊢ 402025020 + 26801668 = 428826688

Proof

Step Hyp Ref Expression
1 4nn0 ⊢ 4 ∈ ℕ 0
2 0nn0 ⊢ 0 ∈ ℕ 0
3 1 2 deccl ⊢ 40 ∈ ℕ 0
4 2nn0 ⊢ 2 ∈ ℕ 0
5 3 4 deccl ⊢ 402 ∈ ℕ 0
6 5 2 deccl ⊢ 4020 ∈ ℕ 0
7 6 4 deccl ⊢ 40202 ∈ ℕ 0
8 5nn0 ⊢ 5 ∈ ℕ 0
9 7 8 deccl ⊢ 402025 ∈ ℕ 0
10 9 2 deccl ⊢ 4020250 ∈ ℕ 0
11 10 4 deccl ⊢ 40202502 ∈ ℕ 0
12 6nn0 ⊢ 6 ∈ ℕ 0
13 4 12 deccl ⊢ 26 ∈ ℕ 0
14 8nn0 ⊢ 8 ∈ ℕ 0
15 13 14 deccl ⊢ 268 ∈ ℕ 0
16 15 2 deccl ⊢ 2680 ∈ ℕ 0
17 1nn0 ⊢ 1 ∈ ℕ 0
18 16 17 deccl ⊢ 26801 ∈ ℕ 0
19 18 12 deccl ⊢ 268016 ∈ ℕ 0
20 19 12 deccl ⊢ 2680166 ∈ ℕ 0
21 eqid ⊢ 402025020 = 402025020
22 eqid ⊢ 26801668 = 26801668
23 eqid ⊢ 40202502 = 40202502
24 eqid ⊢ 2680166 = 2680166
25 eqid ⊢ 4020250 = 4020250
26 eqid ⊢ 268016 = 268016
27 eqid ⊢ 402025 = 402025
28 eqid ⊢ 26801 = 26801
29 eqid ⊢ 40202 = 40202
30 eqid ⊢ 2680 = 2680
31 eqid ⊢ 4020 = 4020
32 eqid ⊢ 268 = 268
33 eqid ⊢ 402 = 402
34 eqid ⊢ 26 = 26
35 eqid ⊢ 40 = 40
36 2cn ⊢ 2 ∈ ℂ
37 36 addlidi ⊢ 0 + 2 = 2
38 1 2 4 35 37 decaddi ⊢ 40 + 2 = 42
39 6cn ⊢ 6 ∈ ℂ
40 6p2e8 ⊢ 6 + 2 = 8
41 39 36 40 addcomli ⊢ 2 + 6 = 8
42 3 4 4 12 33 34 38 41 decadd ⊢ 402 + 26 = 428
43 8cn ⊢ 8 ∈ ℂ
44 43 addlidi ⊢ 0 + 8 = 8
45 5 2 13 14 31 32 42 44 decadd ⊢ 4020 + 268 = 4288
46 36 addridi ⊢ 2 + 0 = 2
47 6 4 15 2 29 30 45 46 decadd ⊢ 40202 + 2680 = 42882
48 5p1e6 ⊢ 5 + 1 = 6
49 7 8 16 17 27 28 47 48 decadd ⊢ 402025 + 26801 = 428826
50 39 addlidi ⊢ 0 + 6 = 6
51 9 2 18 12 25 26 49 50 decadd ⊢ 4020250 + 268016 = 4288266
52 10 4 19 12 23 24 51 41 decadd ⊢ 40202502 + 2680166 = 42882668
53 11 2 20 14 21 22 52 44 decadd ⊢ 402025020 + 26801668 = 428826688