Theorem nnnn0d

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

	Ref	Expression
Hypothesis	nnnn0d.1	$$⊢\phi \to A\in \mathbb{N}$$
Assertion	nnnn0d	$$⊢\phi \to A\in {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		nnnn0d.1	$$⊢\phi \to A\in \mathbb{N}$$
2		nnssnn0	$$⊢\mathbb{N}\subseteq {\mathbb{N}}_0$$
3	2 1	sseldi	$$⊢\phi \to A\in {\mathbb{N}}_0$$