Theorem cxpcld

Description: Closure of the complex power function. (Contributed by Mario Carneiro, 30-May-2016)

	Ref	Expression
Hypotheses	cxp0d.1	|- ( ph -> A e. CC )
	cxpcld.2	|- ( ph -> B e. CC )
Assertion	cxpcld	|- ( ph -> ( A ^c B ) e. CC )

Proof

Step	Hyp	Ref	Expression
1		cxp0d.1	|- ( ph -> A e. CC )
2		cxpcld.2	|- ( ph -> B e. CC )
3		cxpcl	|- ( ( A e. CC /\ B e. CC ) -> ( A ^c B ) e. CC )
4	1 2 3	syl2anc	|- ( ph -> ( A ^c B ) e. CC )