Cancellability of Congruences/Corollary 1/Proof 3

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

Then by definition of congruence:
 * $n \divides k \paren {x - y}$

We have that:
 * $c \perp n$

Thus by Euclid's Lemma:
 * $n \divides \paren {x - y}$

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