Metamath Proof Explorer

Theorem 8nn

Description: 8 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

Ref Expression
Assertion 8nn 
|- 8 e. NN

Proof

Step Hyp Ref Expression
1 df-8 
 |-  8 = ( 7 + 1 )
2 7nn 
 |-  7 e. NN
3 peano2nn 
 |-  ( 7 e. NN -> ( 7 + 1 ) e. NN )
4 2 3 ax-mp 
 |-  ( 7 + 1 ) e. NN
5 1 4 eqeltri 
 |-  8 e. NN