Introduction to group theory/Uniqueness of identity proof

Proof:

Let $G$ be a group, and let $e,e'\in G$ both be identity elements. Then

$\forall a\in G,(a*e=a=e*a)$ and $(a*e'=a=e'*a)$.

Then since $e,e'\in G$

$e=e*e'=e'$ and thus $e=e'$.

Q.E.D.