Theorem nn0negz

Description: The negative of a nonnegative integer is an integer. (Contributed by NM, 9-May-2004)

	Ref	Expression
Assertion	nn0negz	$$⊢N\in {\mathbb{N}}_0\to -N\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		nn0z	$$⊢N\in {\mathbb{N}}_0\to N\in \mathbb{Z}$$
2		znegcl	$$⊢N\in \mathbb{Z}\to -N\in \mathbb{Z}$$
3	1 2	syl	$$⊢N\in {\mathbb{N}}_0\to -N\in \mathbb{Z}$$