Metamath Proof Explorer


Theorem 8t8e64

Description: 8 times 8 equals 64. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 8t8e64 ⊢ 8 ⋅ 8 = 64

Proof

Step Hyp Ref Expression
1 8nn0 ⊢ 8 ∈ ℕ 0
2 7nn0 ⊢ 7 ∈ ℕ 0
3 df-8 ⊢ 8 = 7 + 1
4 8t7e56 ⊢ 8 ⋅ 7 = 56
5 5nn0 ⊢ 5 ∈ ℕ 0
6 6nn0 ⊢ 6 ∈ ℕ 0
7 eqid ⊢ 56 = 56
8 5p1e6 ⊢ 5 + 1 = 6
9 4nn0 ⊢ 4 ∈ ℕ 0
10 1 nn0cni ⊢ 8 ∈ ℂ
11 6 nn0cni ⊢ 6 ∈ ℂ
12 8p6e14 ⊢ 8 + 6 = 14
13 10 11 12 addcomli ⊢ 6 + 8 = 14
14 5 6 1 7 8 9 13 decaddci ⊢ 56 + 8 = 64
15 1 2 3 4 14 4t3lem ⊢ 8 ⋅ 8 = 64