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Metamath Proof Explorer

Theorem negeq0d

Description: A number is zero iff its negative is zero. (Contributed by Mario Carneiro, 27-May-2016)

		Ref	Expression
	Hypothesis	negidd.1	$⊢ φ \to A \in ℂ$
	Assertion	negeq0d	$⊢ φ \to (A = 0 \leftrightarrow - A = 0)$

Step	Hyp	Ref	Expression
1		negidd.1	$⊢ φ \to A \in ℂ$
2		negeq0	$⊢ A \in ℂ \to (A = 0 \leftrightarrow - A = 0)$
3	1 2	syl	$⊢ φ \to (A = 0 \leftrightarrow - A = 0)$