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