Cancellability of Congruences/Corollary 1/Proof 2

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
We are given that $c$ and $n$ are coprime.

So:

Then:

Thus: