Metamath Proof Explorer

Theorem 8p5e13

Description: 8 + 5 = 13. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 8p5e13 
|- ( 8 + 5 ) = ; 1 3

Proof

Step Hyp Ref Expression
1 8nn0 
 |-  8 e. NN0
2 4nn0 
 |-  4 e. NN0
3 2nn0 
 |-  2 e. NN0
4 df-5 
 |-  5 = ( 4 + 1 )
5 df-3 
 |-  3 = ( 2 + 1 )
6 8p4e12 
 |-  ( 8 + 4 ) = ; 1 2
7 1 2 3 4 5 6 6p5lem 
 |-  ( 8 + 5 ) = ; 1 3