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