Real Numbers are Densely Ordered/Proof 2

Corollary to Between two Real Numbers exists Rational Number
Let $a, b \in \R$ be real numbers such that $a < b$.

Then:
 * $\exists r \in \R: a < r < b$

Proof
From Between two Real Numbers exists Rational Number:
 * $\exists r \in \Q: a < r < b$

Since a rational number is also a real number, the result follows by definition.