Ordinals under Multiplication form Ordered Semigroup

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


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

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