Metamath Proof Explorer

Theorem 7t5e35

Description: 7 times 5 equals 35. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 7t5e35 
|- ( 7 x. 5 ) = ; 3 5

Proof

Step Hyp Ref Expression
1 7nn0 
 |-  7 e. NN0
2 4nn0 
 |-  4 e. NN0
3 df-5 
 |-  5 = ( 4 + 1 )
4 7t4e28 
 |-  ( 7 x. 4 ) = ; 2 8
5 2nn0 
 |-  2 e. NN0
6 8nn0 
 |-  8 e. NN0
7 eqid 
 |-  ; 2 8 = ; 2 8
8 2p1e3 
 |-  ( 2 + 1 ) = 3
9 5nn0 
 |-  5 e. NN0
10 8p7e15 
 |-  ( 8 + 7 ) = ; 1 5
11 5 6 1 7 8 9 10 decaddci 
 |-  ( ; 2 8 + 7 ) = ; 3 5
12 1 2 3 4 11 4t3lem 
 |-  ( 7 x. 5 ) = ; 3 5