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.

$\blacksquare$