Theorem nnnn0i

Description: A positive integer is a nonnegative integer. (Contributed by NM, 20-Jun-2005)

	Ref	Expression
Hypothesis	nnnn0i.1	$$⊢N\in \mathbb{N}$$
Assertion	nnnn0i	$$⊢N\in {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		nnnn0i.1	$$⊢N\in \mathbb{N}$$
2		nnnn0	$$⊢N\in \mathbb{N}\to N\in {\mathbb{N}}_0$$
3	1 2	ax-mp	$$⊢N\in {\mathbb{N}}_0$$