Theorem eqnegad

Description: If a complex number equals its own negative, it is zero. One-way deduction form of eqneg . (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Hypotheses	eqnegad.1	|- ( ph -> A e. CC )
	eqnegad.2	|- ( ph -> A = -u A )
Assertion	eqnegad	|- ( ph -> A = 0 )

Proof

Step	Hyp	Ref	Expression
1		eqnegad.1	|- ( ph -> A e. CC )
2		eqnegad.2	|- ( ph -> A = -u A )
3	1	eqnegd	|- ( ph -> ( A = -u A <-> A = 0 ) )
4	2 3	mpbid	|- ( ph -> A = 0 )