Metamath Proof Explorer


Theorem 9t8e72

Description: 9 times 8 equals 72. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 9t8e72 ⊢ 9 ⋅ 8 = 72

Proof

Step Hyp Ref Expression
1 9nn0 ⊢ 9 ∈ ℕ 0
2 7nn0 ⊢ 7 ∈ ℕ 0
3 df-8 ⊢ 8 = 7 + 1
4 9t7e63 ⊢ 9 ⋅ 7 = 63
5 6nn0 ⊢ 6 ∈ ℕ 0
6 3nn0 ⊢ 3 ∈ ℕ 0
7 eqid ⊢ 63 = 63
8 6p1e7 ⊢ 6 + 1 = 7
9 2nn0 ⊢ 2 ∈ ℕ 0
10 9cn ⊢ 9 ∈ ℂ
11 3cn ⊢ 3 ∈ ℂ
12 9p3e12 ⊢ 9 + 3 = 12
13 10 11 12 addcomli ⊢ 3 + 9 = 12
14 5 6 1 7 8 9 13 decaddci ⊢ 63 + 9 = 72
15 1 2 3 4 14 4t3lem ⊢ 9 ⋅ 8 = 72