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 → 𝐴 ∈ ℂ )
Assertion	negeq0d	⊢ ( 𝜑 → ( 𝐴 = 0 ↔ - 𝐴 = 0 ) )

Proof

Step	Hyp	Ref	Expression
1		negidd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		negeq0	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 = 0 ↔ - 𝐴 = 0 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 = 0 ↔ - 𝐴 = 0 ) )