Theorem cxp1

Description: Value of the complex power function at one. (Contributed by Mario Carneiro, 2-Aug-2014)

	Ref	Expression
Assertion	cxp1	$$⊢A\in ℂ\to A^1=A$$

Proof

Step	Hyp	Ref	Expression
1		1nn0	$$⊢1\in {\mathbb{N}}_0$$
2		cxpexp	$$⊢\left(A\in ℂ\wedge 1\in {\mathbb{N}}_0\right)\to A^1=A^1$$
3	1 2	mpan2	$$⊢A\in ℂ\to A^1=A^1$$
4		exp1	$$⊢A\in ℂ\to A^1=A$$
5	3 4	eqtrd	$$⊢A\in ℂ\to A^1=A$$