Ordinals under Multiplication form Ordered Monoid

Theorem
$\struct {\On, \cdot, \le}$ forms an ordered monoid, where:


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

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