# Cancellation Laws/Corollary 1/Proof 1

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## Corollary to Cancellation Laws

- $g h = g \implies h = e$

## Proof

\(\displaystyle g h\) | \(=\) | \(\displaystyle g\) | |||||||||||

\(\displaystyle \leadsto \ \ \) | \(\displaystyle g h\) | \(=\) | \(\displaystyle g e\) | Group Axiom $\text G 2$: Existence of Identity Element | |||||||||

\(\displaystyle \leadsto \ \ \) | \(\displaystyle h\) | \(=\) | \(\displaystyle e\) | Left Cancellation Law |

$\blacksquare$