Doubleton Class of Equal Sets is Singleton Class

Theorem
Let $V$ be a basic universe.

Let $a, b \in V$ be sets.

Consider the doubleton class $\set {a, b}$.

Let $a = b$.

Then:
 * $\set {a, b} = \set a$

where $\set a$ denotes the singleton class of $a$.

Proof
Let $A = \set {a, b}$

The existence of $A$ is shown in Doubleton Class can be Formed from Two Sets:


 * $A := \set {x: \paren {x = a \lor x = b} }$

Let $a = b$.

Then: