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	⊢ ( 𝜑 → 𝐴 ∈ ℕ )
Assertion	peano2nnd	⊢ ( 𝜑 → ( 𝐴 + 1 ) ∈ ℕ )

Proof

Step	Hyp	Ref	Expression
1		nnred.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ )
2		peano2nn	⊢ ( 𝐴 ∈ ℕ → ( 𝐴 + 1 ) ∈ ℕ )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 + 1 ) ∈ ℕ )