Theorem cxp0d

Description: Value of the complex power function when the second argument is zero. (Contributed by Mario Carneiro, 30-May-2016)

	Ref	Expression
Hypothesis	cxp0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	cxp0d	⊢ ( 𝜑 → ( 𝐴 ↑𝑐 0 ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		cxp0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		cxp0	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 ↑𝑐 0 ) = 1 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ↑𝑐 0 ) = 1 )