Metamath Proof Explorer

Theorem 3nn

Description: 3 is a positive integer. (Contributed by NM, 8-Jan-2006)

Ref Expression
Assertion 3nn 
|- 3 e. NN

Proof

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