# Identity of Subgroup

## Theorem

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

Let $H$ be a subgroup of group $G$.

Then the identity of $H$ is also $e$.

## Proof

From the Cancellation Laws, all of its elements are cancellable.

The result then follows from Identity of Cancellable Monoid is Identity of Submonoid.

$\blacksquare$