Ordinals under Multiplication form Semigroup

Theorem
$\left({\operatorname{On}, \cdot}\right)$ forms an semigroup, where:


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

Proof
The result follows from Ordinal Multiplication is Closed and Ordinal Multiplication is Associative.