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	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	eqnegd	⊢ ( 𝜑 → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) )

Proof

Step	Hyp	Ref	Expression
1		eqnegd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		eqneg	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) )