How do we know the Gamma function Γ(n-1)?

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We know that $\Gamma(n)=(n−1)!$ and I do not know how $\Gamma(n-1)$ equal to? Is there a proof for that. I tried and got $\Gamma(n-1)= n\Gamma(n)$ but I'm not sure is correct or not

Is there any proof or formal that will help??