Metamath Proof Explorer

Theorem 4nn

Description: 4 is a positive integer. (Contributed by NM, 8-Jan-2006)

Ref Expression
Assertion 4nn 
|- 4 e. NN

Proof

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