Theorem eqnegad

Description: If a complex number equals its own negative, it is zero. One-way deduction form of eqneg . (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypotheses	eqnegad.1	$$⊢\phi \to A\in ℂ$$
	eqnegad.2	$$⊢\phi \to A=-A$$
Assertion	eqnegad	$$⊢\phi \to A=0$$

Proof

Step	Hyp	Ref	Expression
1		eqnegad.1	$$⊢\phi \to A\in ℂ$$
2		eqnegad.2	$$⊢\phi \to A=-A$$
3	1	eqnegd	$$⊢\phi \to \left(A=-A\leftrightarrow A=0\right)$$
4	2 3	mpbid	$$⊢\phi \to A=0$$