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Metamath Proof Explorer

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	$⊢ A \neq 0 \leftrightarrow - A \neq 0$

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