Every partial ordering $\displaystyle \leq$ on a set $\displaystyle P$ has a linearization, i.e., some linear ordering $\displaystyle \leq'$ of $\displaystyle P$ exists such that $\displaystyle x \leq y \Rightarrow x \leq' y$.

This exercise indicates to use the axiom of choice. I do not see how to prove this. I know that a partial ordered set is reflexive, transitive, and antisymmetric. However, I don't see how this has a linearization. I need a few pointers. Thanks.