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

$\blacksquare$