Axiom:Axiom of Unions

For every collection of sets, there exists a set (the sum or union set) that contains all the elements that belong to at least one of the sets in the collection:


 * $$\forall A: \exists x: \forall y: \left({y \in x \iff \exists z: \left({z \in A \and y \in z}\right)}\right)$$

Otherwise known as the Axiom of the Sum Set.