Theorem peano2zd

Description: Deduction from second Peano postulate generalized to integers. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	zred.1	|- ( ph -> A e. ZZ )
Assertion	peano2zd	|- ( ph -> ( A + 1 ) e. ZZ )

Proof

Step	Hyp	Ref	Expression
1		zred.1	|- ( ph -> A e. ZZ )
2		peano2z	|- ( A e. ZZ -> ( A + 1 ) e. ZZ )
3	1 2	syl	|- ( ph -> ( A + 1 ) e. ZZ )