Ordinals under Addition form Ordered Monoid

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


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

Proof
The result follows from Ordinals under Addition form Monoid and Ordinals under Addition form Ordered Semigroup.