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	$$⊢\phi \to A\in ℂ$$
	cxpefd.2	$$⊢\phi \to A\ne 0$$
Assertion	0cxpd	$$⊢\phi \to 0^A=0$$

Proof

Step	Hyp	Ref	Expression
1		cxp0d.1	$$⊢\phi \to A\in ℂ$$
2		cxpefd.2	$$⊢\phi \to A\ne 0$$
3		0cxp	$$⊢\left(A\in ℂ\wedge A\ne 0\right)\to 0^A=0$$
4	1 2 3	syl2anc	$$⊢\phi \to 0^A=0$$