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	$$⊢\phi \to A\in \mathbb{N}$$
Assertion	peano2nnd	$$⊢\phi \to A+1\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		nnred.1	$$⊢\phi \to A\in \mathbb{N}$$
2		peano2nn	$$⊢A\in \mathbb{N}\to A+1\in \mathbb{N}$$
3	1 2	syl	$$⊢\phi \to A+1\in \mathbb{N}$$