# Even Order Group has Order 2 Element/Proof 2

## 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.

$\blacksquare$