Cancellability of Congruences/Corollary 1/Proof 3

Proof
Let:
 * $c a \equiv c b \pmod n$

Then by definition of congruence:
 * $n \mathrel \backslash k \left({x - y}\right)$

We have that:
 * $c \perp n$

Thus by Euclid's Lemma:
 * $n \mathrel \backslash \left({x - y}\right)$

So by definition of congruence:
 * $a \equiv b \pmod n$