Triangle Inequality/Real Numbers/Proof 3

Theorem
Let $x, y \in \R$ be real numbers.

Let $\left\vert{x}\right\vert$ be the absolute value of $x$.

Then:
 * $\left\vert{x + y}\right\vert \le \left\vert{x}\right\vert + \left\vert{y}\right\vert$

Proof
From Real Numbers form Ordered Integral Domain, we can directly apply Sum of Absolute Values, which is applicable on all ordered integral domains, of which $\R$ is one.

Note that this result can not directly be used for the complex numbers $\C$ as they do not form an ordered integral domain.