Metamath Proof Explorer

Theorem 9t7e63

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

Ref Expression
Assertion 9t7e63 
|- ( 9 x. 7 ) = ; 6 3

Proof

Step Hyp Ref Expression
1 9nn0 
 |-  9 e. NN0
2 6nn0 
 |-  6 e. NN0
3 df-7 
 |-  7 = ( 6 + 1 )
4 9t6e54 
 |-  ( 9 x. 6 ) = ; 5 4
5 5nn0 
 |-  5 e. NN0
6 4nn0 
 |-  4 e. NN0
7 eqid 
 |-  ; 5 4 = ; 5 4
8 5p1e6 
 |-  ( 5 + 1 ) = 6
9 3nn0 
 |-  3 e. NN0
10 1 nn0cni 
 |-  9 e. CC
11 6 nn0cni 
 |-  4 e. CC
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 x. 7 ) = ; 6 3