Stabilizer is Subgroup/Corollary

Corollary to Stabilizer is Subgroup
Let $G$ be a group whose identity is $e$.

Let $G$ act on a set $X$.

Let $x \in X$.

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