Theorem eqnegd

Description: A complex number equals its negative iff it is zero. Deduction form of eqneg . (Contributed by David Moews, 28-Feb-2017)

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

Proof

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