Ordinals under Addition form Ordered Semigroup

Theorem
$\left({\operatorname{On}, +, \le}\right)$ forms an ordered semigroup, where:


 * $\operatorname{On}$ denotes the ordinal class, and
 * $+$ denotes ordinal addition.

Proof
The result follows from Ordinals under Addition form Semigroup and Subset is Compatible with Ordinal Addition.