Metamath Proof Explorer

Theorem peano2z

Description: Second Peano postulate generalized to integers. (Contributed by NM, 13-Feb-2005)

Ref Expression
Assertion peano2z 
|- ( N e. ZZ -> ( N + 1 ) e. ZZ )

Proof

Step Hyp Ref Expression
1 1z 
 |-  1 e. ZZ
2 zaddcl 
 |-  ( ( N e. ZZ /\ 1 e. ZZ ) -> ( N + 1 ) e. ZZ )
3 1 2 mpan2 
 |-  ( N e. ZZ -> ( N + 1 ) e. ZZ )