Theorem negeq0d

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

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

Proof

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