Ordinals under Multiplication form Ordered Monoid

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


 * $\On$ denotes the class of all ordinals
 * $\times$ denotes ordinal multiplication.

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