Singleton Class of Set is Set

Theorem
Let $x$ be a set.

Then the singleton class $\set x$ is likewise a set.

Proof
Let $x$ and $y$ be sets.

Let $x = y$.

From Doubleton Class of Equal Sets is Singleton Class, the doubleton class $\set {x, y}$ is the singleton class $\set x$.

From the axiom of pairing, the doubleton class $\set {x, y}$ is a set when $x$ and $y$ are sets.

Hence $\set x$ is a set.