Unit of Integral Domain divides all Elements

Theorem
Let $\struct {D, +, \circ}$ be an integral domain whose unity is $1_D$.

Let $\struct {U_D, \circ}$ be the group of units of $\struct {D, +, \circ}$.

Then:
 * $\forall x \in D: \forall u \in U_D: u \divides x$

That is, every unit of $D$ is a divisor of every element of $D$.