Cancellability of Congruences/Corollary 1/Proof 1

Corollary to Cancellability of Congruences
Let $c$ and $n$ be coprime integers, i.e. $c \perp n$.

Then:


 * $c a \equiv c b \pmod n \implies a \equiv b \pmod n$

where $\equiv$ denotes congruence.

Proof
Recall that $c \perp n$ means $\gcd \left\{{c, n}\right\} = 1$.

The result follows directly from Cancellability of Congruences.