Metamath Proof Explorer

Theorem 8t7e56

Description: 8 times 7 equals 56. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 8t7e56 
|- ( 8 x. 7 ) = ; 5 6

Proof

Step Hyp Ref Expression
1 8nn0 
 |-  8 e. NN0
2 6nn0 
 |-  6 e. NN0
3 df-7 
 |-  7 = ( 6 + 1 )
4 8t6e48 
 |-  ( 8 x. 6 ) = ; 4 8
5 4nn0 
 |-  4 e. NN0
6 eqid 
 |-  ; 4 8 = ; 4 8
7 4p1e5 
 |-  ( 4 + 1 ) = 5
8 8p8e16 
 |-  ( 8 + 8 ) = ; 1 6
9 5 1 1 6 7 2 8 decaddci 
 |-  ( ; 4 8 + 8 ) = ; 5 6
10 1 2 3 4 9 4t3lem 
 |-  ( 8 x. 7 ) = ; 5 6