Theorem nn0negzi

Description: The negative of a nonnegative integer is an integer. (Contributed by Mario Carneiro, 18-Feb-2014)

	Ref	Expression
Hypothesis	nn0negzi.1	$$⊢N\in {\mathbb{N}}_0$$
Assertion	nn0negzi	$$⊢-N\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		nn0negzi.1	$$⊢N\in {\mathbb{N}}_0$$
2		nn0negz	$$⊢N\in {\mathbb{N}}_0\to -N\in \mathbb{Z}$$
3	1 2	ax-mp	$$⊢-N\in \mathbb{Z}$$