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Metamath Proof Explorer

Theorem nnnn0d

Description: A positive integer is a nonnegative integer. (Contributed by Mario Carneiro, 27-May-2016)

		Ref	Expression
	Hypothesis	nnnn0d.1	$⊢ φ \to A \in ℕ$
	Assertion	nnnn0d	$⊢ φ \to A \in ℕ_{0}$

Step	Hyp	Ref	Expression
1		nnnn0d.1	$⊢ φ \to A \in ℕ$
2		nnssnn0	$⊢ ℕ \subseteq ℕ_{0}$
3	2 1	sselid	$⊢ φ \to A \in ℕ_{0}$