Metamath Proof Explorer

Theorem 8t8e64

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

Ref Expression
Assertion 8t8e64 
|- ( 8 x. 8 ) = ; 6 4

Proof

Step Hyp Ref Expression
1 8nn0 
 |-  8 e. NN0
2 7nn0 
 |-  7 e. NN0
3 df-8 
 |-  8 = ( 7 + 1 )
4 8t7e56 
 |-  ( 8 x. 7 ) = ; 5 6
5 5nn0 
 |-  5 e. NN0
6 6nn0 
 |-  6 e. NN0
7 eqid 
 |-  ; 5 6 = ; 5 6
8 5p1e6 
 |-  ( 5 + 1 ) = 6
9 4nn0 
 |-  4 e. NN0
10 1 nn0cni 
 |-  8 e. CC
11 6 nn0cni 
 |-  6 e. CC
12 8p6e14 
 |-  ( 8 + 6 ) = ; 1 4
13 10 11 12 addcomli 
 |-  ( 6 + 8 ) = ; 1 4
14 5 6 1 7 8 9 13 decaddci 
 |-  ( ; 5 6 + 8 ) = ; 6 4
15 1 2 3 4 14 4t3lem 
 |-  ( 8 x. 8 ) = ; 6 4