Theorem cjne0d

Description: A number is nonzero iff its complex conjugate is nonzero. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypotheses	recld.1	|- ( ph -> A e. CC )
	cjne0d.2	|- ( ph -> A =/= 0 )
Assertion	cjne0d	|- ( ph -> ( * ` A ) =/= 0 )

Proof

Step	Hyp	Ref	Expression
1		recld.1	|- ( ph -> A e. CC )
2		cjne0d.2	|- ( ph -> A =/= 0 )
3		cjne0	|- ( A e. CC -> ( A =/= 0 <-> ( * ` A ) =/= 0 ) )
4	1 3	syl	|- ( ph -> ( A =/= 0 <-> ( * ` A ) =/= 0 ) )
5	2 4	mpbid	|- ( ph -> ( * ` A ) =/= 0 )