Theorem eqnegi

Description: A number equal to its negative is zero. (Contributed by NM, 29-May-1999)

	Ref	Expression
Hypothesis	divclz.1	⊢ 𝐴 ∈ ℂ
Assertion	eqnegi	⊢ ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	⊢ 𝐴 ∈ ℂ
2		eqneg	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 ) )
3	1 2	ax-mp	⊢ ( 𝐴 = - 𝐴 ↔ 𝐴 = 0 )