Theorem negne0bi

Description: A number is nonzero iff its negative is nonzero. (Contributed by NM, 10-Aug-1999)

	Ref	Expression
Hypothesis	negidi.1	$$⊢A\in ℂ$$
Assertion	negne0bi	$$⊢A\ne 0\leftrightarrow -A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		negeq0	$$⊢A\in ℂ\to \left(A=0\leftrightarrow -A=0\right)$$
3	1 2	ax-mp	$$⊢A=0\leftrightarrow -A=0$$
4	3	necon3bii	$$⊢A\ne 0\leftrightarrow -A\ne 0$$