Axiom:Axiom of Unions/Set Theory

Axiom
For every set of sets $A$, there exists a set $x$ (the union set) that contains all and only those elements that belong to at least one of the sets in the $A$:


 * $\forall A: \exists x: \forall y: \paren {y \in x \iff \exists z: \paren {z \in A \land y \in z} }$

Also see

 * Equivalence of Formulations of Axiom of Unions


 * Definition:Union of Set of Sets


 * Axiom:Axiom of Unions (Class Theory)