Theorem exp0d

Description: Value of a complex number raised to the zeroth power. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	expcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	exp0d	⊢ ( 𝜑 → ( 𝐴 ↑ 0 ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		expcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		exp0	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 ↑ 0 ) = 1 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ↑ 0 ) = 1 )