Ordinals under Multiplication form Ordered Semigroup

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


 * $\operatorname{On}$ denotes the ordinal class, and
 * $\cdot$ denotes ordinal multiplication.

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