Ordinals under Addition form Ordered Semigroup

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


 * $\On$ denotes the class of all ordinals
 * $+$ denotes ordinal addition.

Proof
The result follows from:
 * Ordinals under Addition form Semigroup
 * Subset is Compatible with Ordinal Addition.