Axiom:Axiom of Abstraction

Axiom
The  states:
 * Given any property $P$, there exists a unique set which consists of all and only those objects which have property $P$:


 * $\set {x: \map P x}$

From the definition of a set:


 * A set is any aggregation of objects, called elements, which can be precisely defined in some way or other.

Also see

 * Definition:Set Definition by Predicate