Power Set can be Derived using Axiom of Abstraction

Theorem
Let $a$ be a set.

By application of the, the power set $\powerset a$ can be formed.

Hence the power set $\powerset a$ can be derived as a valid object in Frege set theory.

Proof
Let $P$ be the property defined as:


 * $\forall x: \map P x := \paren {x \subseteq a}$

where $\lor$ is the disjunction operator.

Hence, using the, we form the set:
 * $\powerset a := \set {x: x \subseteq a}$