# Stabilizer is Subgroup/Corollary 1

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## Corollary to Stabilizer is Subgroup

Let $G$ be a group whose identity is $e$.

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

Then:

$\forall x \in X: e \in \Stab x$

## Proof

Follows directly from Stabilizer is Subgroup and Identity of Subgroup.