# Identity of Group is Unique/Proof 1

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## Theorem

Let $\struct {G, \circ}$ be a group which has an identity element $e \in G$.

Then $e$ is unique.

## Proof

By the definition of a group, $\struct {G, \circ}$ is also a monoid.

The result follows by applying the result Identity of Monoid is Unique.

$\blacksquare$

## Sources

- 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 33.1$. The definition of a group