Theorem cxp1d

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

	Ref	Expression
Hypothesis	cxp0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	cxp1d	⊢ ( 𝜑 → ( 𝐴 ↑𝑐 1 ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		cxp0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		cxp1	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 ↑𝑐 1 ) = 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ↑𝑐 1 ) = 𝐴 )