Theorem znegcld

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

	Ref	Expression
Hypothesis	zred.1	$$⊢\phi \to A\in \mathbb{Z}$$
Assertion	znegcld	$$⊢\phi \to -A\in \mathbb{Z}$$

Proof

Step	Hyp	Ref	Expression
1		zred.1	$$⊢\phi \to A\in \mathbb{Z}$$
2		znegcl	$$⊢A\in \mathbb{Z}\to -A\in \mathbb{Z}$$
3	1 2	syl	$$⊢\phi \to -A\in \mathbb{Z}$$