# Even Order Group has Order 2 Element/Proof 2

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## Theorem

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

Let $G$ be of even order.

Then:

- $\exists x \in G: \order x = 2$

That is:

- $\exists x \in G: x \ne e: x^2 = e$

## Proof

This is a direct corollary of the stronger result Even Order Group has Odd Number of Order 2 Elements.

$\blacksquare$