Ordinals under Multiplication form Monoid

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


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

Proof
The result follows from Ordinals under Multiplication form Semigroup and Ordinal Multiplication by One.