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	|- ( ph -> A e. CC )
Assertion	eqnegd	|- ( ph -> ( A = -u A <-> A = 0 ) )

Proof

Step	Hyp	Ref	Expression
1		eqnegd.1	|- ( ph -> A e. CC )
2		eqneg	|- ( A e. CC -> ( A = -u A <-> A = 0 ) )
3	1 2	syl	|- ( ph -> ( A = -u A <-> A = 0 ) )