Theorem eqnegi

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

	Ref	Expression
Hypothesis	divclz.1	$$⊢A\in ℂ$$
Assertion	eqnegi	$$⊢A=-A\leftrightarrow A=0$$

Proof

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