Metamath Proof Explorer

Theorem 5nn

Description: 5 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

Ref Expression
Assertion 5nn 
|- 5 e. NN

Proof

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