Ordering of Reciprocals

Theorem
Let $x, y \in \R$ be real numbers such that $x,y \in \left({0 \,.\,.\, \to}\right)$ or $x,y \in \left({\gets \,.\,.\, 0}\right)$

Then:
 * $x \le y \iff \dfrac 1 y \le \dfrac 1 x$