Theorem 0cxpd

Description: Value of the complex power function when the first argument is zero. (Contributed by Mario Carneiro, 30-May-2016)

	Ref	Expression
Hypotheses	cxp0d.1	|- ( ph -> A e. CC )
	cxpefd.2	|- ( ph -> A =/= 0 )
Assertion	0cxpd	|- ( ph -> ( 0 ^c A ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		cxp0d.1	|- ( ph -> A e. CC )
2		cxpefd.2	|- ( ph -> A =/= 0 )
3		0cxp	|- ( ( A e. CC /\ A =/= 0 ) -> ( 0 ^c A ) = 0 )
4	1 2 3	syl2anc	|- ( ph -> ( 0 ^c A ) = 0 )