Theorem numexp0

Description: Calculate an integer power. (Contributed by Mario Carneiro, 17-Apr-2015)

	Ref	Expression
Hypothesis	numexp.1	⊢ 𝐴 ∈ ℕ0
Assertion	numexp0	⊢ ( 𝐴 ↑ 0 ) = 1

Proof

Step	Hyp	Ref	Expression
1		numexp.1	⊢ 𝐴 ∈ ℕ0
2	1	nn0cni	⊢ 𝐴 ∈ ℂ
3		exp0	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 ↑ 0 ) = 1 )
4	2 3	ax-mp	⊢ ( 𝐴 ↑ 0 ) = 1