Zero is Smallest Ordinal

Theorem
The natural number $0$ is the smallest ordinal.

Proof
Let $\On$ denote the class of all ordinals.

By Zero is Ordinal, $0$ is an element of $\On$.

We identify the natural number $0$ via the von Neumann construction of the natural numbers as:
 * $0 := \O$

By Empty Class is Subclass of All Classes:
 * $\forall \alpha \in \On: \O \subseteq \alpha$

Hence the result by definition of smallest element.