Theorem negne0i

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

	Ref	Expression
Hypotheses	negidi.1	⊢ 𝐴 ∈ ℂ
	negne0i.2	⊢ 𝐴 ≠ 0
Assertion	negne0i	⊢ - 𝐴 ≠ 0

Proof

Step	Hyp	Ref	Expression
1		negidi.1	⊢ 𝐴 ∈ ℂ
2		negne0i.2	⊢ 𝐴 ≠ 0
3	1	negne0bi	⊢ ( 𝐴 ≠ 0 ↔ - 𝐴 ≠ 0 )
4	2 3	mpbi	⊢ - 𝐴 ≠ 0