Theorem negne0i

Description: The negative of a nonzero number is nonzero. (Contributed by NM, 30-Jul-2004)

	Ref	Expression
Hypotheses	negidi.1	$$⊢A\in ℂ$$
	negne0i.2	$$⊢A\ne 0$$
Assertion	negne0i	$$⊢-A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		negne0i.2	$$⊢A\ne 0$$
3	1	negne0bi	$$⊢A\ne 0\leftrightarrow -A\ne 0$$
4	2 3	mpbi	$$⊢-A\ne 0$$