Metamath Proof Explorer

Theorem 7p5e12

Description: 7 + 5 = 12. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 7p5e12 
|- ( 7 + 5 ) = ; 1 2

Proof

Step Hyp Ref Expression
1 7nn0 
 |-  7 e. NN0
2 4nn0 
 |-  4 e. NN0
3 1nn0 
 |-  1 e. NN0
4 df-5 
 |-  5 = ( 4 + 1 )
5 df-2 
 |-  2 = ( 1 + 1 )
6 7p4e11 
 |-  ( 7 + 4 ) = ; 1 1
7 1 2 3 4 5 6 6p5lem 
 |-  ( 7 + 5 ) = ; 1 2