Theorem cxp0

Description: Value of the complex power function when the second argument is zero. (Contributed by Mario Carneiro, 2-Aug-2014)

	Ref	Expression
Assertion	cxp0	$$⊢A\in ℂ\to A^0=1$$

Proof

Step	Hyp	Ref	Expression
1		0nn0	$$⊢0\in {\mathbb{N}}_0$$
2		cxpexp	$$⊢\left(A\in ℂ\wedge 0\in {\mathbb{N}}_0\right)\to A^0=A^0$$
3	1 2	mpan2	$$⊢A\in ℂ\to A^0=A^0$$
4		exp0	$$⊢A\in ℂ\to A^0=1$$
5	3 4	eqtrd	$$⊢A\in ℂ\to A^0=1$$