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 ∈ ℕ0
Assertion	nn0negzi	⊢ - 𝑁 ∈ ℤ

Proof

Step	Hyp	Ref	Expression
1		nn0negzi.1	⊢ 𝑁 ∈ ℕ0
2		nn0negz	⊢ ( 𝑁 ∈ ℕ0 → - 𝑁 ∈ ℤ )
3	1 2	ax-mp	⊢ - 𝑁 ∈ ℤ