Metamath Proof Explorer

Theorem 6nn

Description: 6 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

Ref Expression
Assertion 6nn 
|- 6 e. NN

Proof

Step Hyp Ref Expression
1 df-6 
 |-  6 = ( 5 + 1 )
2 5nn 
 |-  5 e. NN
3 peano2nn 
 |-  ( 5 e. NN -> ( 5 + 1 ) e. NN )
4 2 3 ax-mp 
 |-  ( 5 + 1 ) e. NN
5 1 4 eqeltri 
 |-  6 e. NN