Metamath Proof Explorer

Theorem 9p4e13

Description: 9 + 4 = 13. (Contributed by Mario Carneiro, 19-Apr-2015)

Ref Expression
Assertion 9p4e13 
|- ( 9 + 4 ) = ; 1 3

Proof

Step Hyp Ref Expression
1 9nn0 
 |-  9 e. NN0
2 3nn0 
 |-  3 e. NN0
3 2nn0 
 |-  2 e. NN0
4 df-4 
 |-  4 = ( 3 + 1 )
5 df-3 
 |-  3 = ( 2 + 1 )
6 9p3e12 
 |-  ( 9 + 3 ) = ; 1 2
7 1 2 3 4 5 6 6p5lem 
 |-  ( 9 + 4 ) = ; 1 3