Theorem nn0negz

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

	Ref	Expression
Assertion	nn0negz	⊢ ( 𝑁 ∈ ℕ0 → - 𝑁 ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		nn0z	⊢ ( 𝑁 ∈ ℕ0 → 𝑁 ∈ ℤ )
2		znegcl	⊢ ( 𝑁 ∈ ℤ → - 𝑁 ∈ ℤ )
3	1 2	syl	⊢ ( 𝑁 ∈ ℕ0 → - 𝑁 ∈ ℤ )