Theorem gamcl

Description: The exponential of the log-Gamma function is the Gamma function (by definition). (Contributed by Mario Carneiro, 8-Jul-2017)

	Ref	Expression
Assertion	gamcl	⊢ ( 𝐴 ∈ ( ℂ ∖ ( ℤ ∖ ℕ ) ) → ( Γ ‘ 𝐴 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		gamf	⊢ Γ : ( ℂ ∖ ( ℤ ∖ ℕ ) ) ⟶ ℂ
2	1	ffvelrni	⊢ ( 𝐴 ∈ ( ℂ ∖ ( ℤ ∖ ℕ ) ) → ( Γ ‘ 𝐴 ) ∈ ℂ )