Metamath Proof Explorer

Theorem 7p6e13

Description: 7 + 6 = 13. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 7p6e13 
|- ( 7 + 6 ) = ; 1 3

Proof

Step Hyp Ref Expression
1 7nn0 
 |-  7 e. NN0
2 5nn0 
 |-  5 e. NN0
3 2nn0 
 |-  2 e. NN0
4 df-6 
 |-  6 = ( 5 + 1 )
5 df-3 
 |-  3 = ( 2 + 1 )
6 7p5e12 
 |-  ( 7 + 5 ) = ; 1 2
7 1 2 3 4 5 6 6p5lem 
 |-  ( 7 + 6 ) = ; 1 3