Theorem peano2nnd

Description: Peano postulate: a successor of a positive integer is a positive integer. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	nnred.1	|- ( ph -> A e. NN )
Assertion	peano2nnd	|- ( ph -> ( A + 1 ) e. NN )

Proof

Step	Hyp	Ref	Expression
1		nnred.1	|- ( ph -> A e. NN )
2		peano2nn	|- ( A e. NN -> ( A + 1 ) e. NN )
3	1 2	syl	|- ( ph -> ( A + 1 ) e. NN )