Metamath Proof Explorer


Theorem 9t7e63

Description: 9 times 7 equals 63. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 9t7e63 ( 9 · 7 ) = 6 3

Proof

Step Hyp Ref Expression
1 9nn0 ⊢ 9 ∈ ℕ0
2 6nn0 ⊢ 6 ∈ ℕ0
3 df-7 ⊢ 7 = ( 6 + 1 )
4 9t6e54 ⊢ ( 9 · 6 ) = 5 4
5 5nn0 ⊢ 5 ∈ ℕ0
6 4nn0 ⊢ 4 ∈ ℕ0
7 eqid ⊢ 5 4 = 5 4
8 5p1e6 ⊢ ( 5 + 1 ) = 6
9 3nn0 ⊢ 3 ∈ ℕ0
10 1 nn0cni ⊢ 9 ∈ ℂ
11 6 nn0cni ⊢ 4 ∈ ℂ
12 9p4e13 ⊢ ( 9 + 4 ) = 1 3
13 10 11 12 addcomli ⊢ ( 4 + 9 ) = 1 3
14 5 6 1 7 8 9 13 decaddci ⊢ ( 5 4 + 9 ) = 6 3
15 1 2 3 4 14 4t3lem ⊢ ( 9 · 7 ) = 6 3