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	$$⊢A\in \left(ℂ\setminus \left(\mathbb{Z}\setminus \mathbb{N}\right)\right)\to \mathrm{\Gamma }\left(A\right)\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		gamf	$$⊢\mathrm{\Gamma }:ℂ\setminus \left(\mathbb{Z}\setminus \mathbb{N}\right)⟶ℂ$$
2	1	ffvelrni	$$⊢A\in \left(ℂ\setminus \left(\mathbb{Z}\setminus \mathbb{N}\right)\right)\to \mathrm{\Gamma }\left(A\right)\in ℂ$$