Stabilizer is Subgroup/Corollary

Stabilizer is Subgroup: Corollary
Let $G$ be a group whose identity is $e$, which acts on a set $X$.

Then:
 * $\forall g, h \in G: g * x = h * x \iff g^{-1} h \in \operatorname{Stab} \left({x}\right)$