Theorem znegcld

Description: Closure law for negative integers. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	zred.1	⊢ ( 𝜑 → 𝐴 ∈ ℤ )
Assertion	znegcld	⊢ ( 𝜑 → - 𝐴 ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		zred.1	⊢ ( 𝜑 → 𝐴 ∈ ℤ )
2		znegcl	⊢ ( 𝐴 ∈ ℤ → - 𝐴 ∈ ℤ )
3	1 2	syl	⊢ ( 𝜑 → - 𝐴 ∈ ℤ )