Cancellation Laws/Corollary 1/Proof 1
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Corollary to Cancellation Laws
- $g h = g \implies h = e$
Proof
| \(\ds g h\) | \(=\) | \(\ds g\) | ||||||||||||
| \(\ds \leadsto \ \ \) | \(\ds g h\) | \(=\) | \(\ds g e\) | Group Axiom $\text G 2$: Existence of Identity Element | ||||||||||
| \(\ds \leadsto \ \ \) | \(\ds h\) | \(=\) | \(\ds e\) | Left Cancellation Law |
$\blacksquare$