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Metamath Proof Explorer

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	$⊢ φ \to A \in ℕ$
	Assertion	peano2nnd	$⊢ φ \to A + 1 \in ℕ$

Step	Hyp	Ref	Expression
1		nnred.1	$⊢ φ \to A \in ℕ$
2		peano2nn	$⊢ A \in ℕ \to A + 1 \in ℕ$
3	1 2	syl	$⊢ φ \to A + 1 \in ℕ$