Ordinal is Subset of Successor

Theorem
Let $x$ and $y$ be ordinals.

Let $x^+$ denote the successor of $x$.

Then:
 * $x \subseteq y^+ \iff \left({x \subseteq y \lor x = y^+}\right)$

Proof
Let $A \subset B$ denote that $A$ is a proper subset of $B$.

Let $A \in B$ denote that $A$ is an element of $B$.

From Transitive Set is Proper Subset of Ordinal iff Element of Ordinal, $\subset$ and $\in$ can be used interchangeably.

Thus:

Conversely: