Subset is Compatible with Ordinal Addition

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

Then:


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

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