Theorem cxp1

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

	Ref	Expression
Assertion	cxp1	|- ( A e. CC -> ( A ^c 1 ) = A )

Proof

Step	Hyp	Ref	Expression
1		1nn0	|- 1 e. NN0
2		cxpexp	|- ( ( A e. CC /\ 1 e. NN0 ) -> ( A ^c 1 ) = ( A ^ 1 ) )
3	1 2	mpan2	|- ( A e. CC -> ( A ^c 1 ) = ( A ^ 1 ) )
4		exp1	|- ( A e. CC -> ( A ^ 1 ) = A )
5	3 4	eqtrd	|- ( A e. CC -> ( A ^c 1 ) = A )