Subset is Compatible with Ordinal Addition

Theorem
Let $x, y, z$ be ordinals.

Then:


 * $(1): x \le y \implies \left({z + x}\right) \le \left({z + y}\right)$
 * $(2): x \le y \implies \left({x + z}\right) \le \left({y + z}\right)$

Proof
The result follows from Subset is Left Compatible with Ordinal Addition and Subset is Right Compatible with Ordinal Addition.