Class of All Ordinals is Proper Class
Let $\On$ denote the class of all ordinals.
Then $\On$ is a proper class.
That is, $\On$ is not a set.
We have that Successor Mapping on Ordinals is Strictly Progressing.
The result follows from Superinductive Class under Strictly Progressing Mapping is Proper Class.
Hence $\On$ is a proper class.