Metamath Proof Explorer

Theorem 8p4e12

Description: 8 + 4 = 12. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 8p4e12 
|- ( 8 + 4 ) = ; 1 2

Proof

Step Hyp Ref Expression
1 8nn0 
 |-  8 e. NN0
2 3nn0 
 |-  3 e. NN0
3 1nn0 
 |-  1 e. NN0
4 df-4 
 |-  4 = ( 3 + 1 )
5 df-2 
 |-  2 = ( 1 + 1 )
6 8p3e11 
 |-  ( 8 + 3 ) = ; 1 1
7 1 2 3 4 5 6 6p5lem 
 |-  ( 8 + 4 ) = ; 1 2