Class of All Ordinals is G-Tower

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

Let $g$ be the successor mapping:
 * $\forall x \in \On: \map g x = x \cup \set x$

Then $\On$ is a $g$-tower.

Proof
From Successor Mapping is Progressing, $g$ is a progressing mapping.

From Class of All Ordinals is Minimally Superinductive over Successor Mapping, $\On$ is superinductive over $g$.

Hence the result by definition of $g$-tower.