Using a specific Lemma, how to prove that between any two distinct rational numbers there exists an irrational number?

Lemma: If $m/n$ and $r/s$ are rational, with $r/s\ne 0$, then $r/s\ne 0$ is irrational.

Lemma: If $m/n$ and $r/s$ are rational, with $r/s\ne 0$, then $r/s\ne 0$ is irrational.