# Cancellation Laws/Corollary 1/Proof 1

$g h = g \implies h = e$
 $\displaystyle g h$ $=$ $\displaystyle g$ $\displaystyle \leadsto \ \$ $\displaystyle g h$ $=$ $\displaystyle g e$ Group Axiom $\text G 2$: Existence of Identity Element $\displaystyle \leadsto \ \$ $\displaystyle h$ $=$ $\displaystyle e$ Left Cancellation Law
$\blacksquare$