Theorem negne0d

Description: The negative of a nonzero number is nonzero. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypotheses	negidd.1	$$⊢\phi \to A\in ℂ$$
	negne0d.2	$$⊢\phi \to A\ne 0$$
Assertion	negne0d	$$⊢\phi \to -A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		negidd.1	$$⊢\phi \to A\in ℂ$$
2		negne0d.2	$$⊢\phi \to A\ne 0$$
3	1	negne0bd	$$⊢\phi \to \left(A\ne 0\leftrightarrow -A\ne 0\right)$$
4	2 3	mpbid	$$⊢\phi \to -A\ne 0$$