Between two Rational Numbers exists Irrational Number/Proof 2

Proof
From Between two Real Numbers exists Rational Number, there exists $x \in \Q$ such that:
 * $a - \sqrt2 < x < b - \sqrt2$

Since Square Root of 2 is Irrational, by the Lemma:
 * $x + \sqrt 2$ is irrational.

But:
 * $a < x + \sqrt 2 < b$

which is what we wanted to show.