Singleton Class can be Formed from Set

Theorem
Let $V$ be a basic universe.

Let $a \in V$ be a set.

Then the singleton class $\set a$ can be formed, which is a subclass of $V$.

Proof
Using the axiom of specification, let $A$ be the class defined as:
 * $A := \set {x: x \in V \land x = a}$

That is:
 * $A = \set a$

By the axiom of extension, $\set a$ is the only such class which has $a$ as an element.

Also see

 * Definition:Singleton Class