Category:Axioms/Axiom of Unions

This category contains axioms related to Axiom of Unions.

Set Theory

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 $A$:

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

Class Theory

Let $x$ be a set (of sets).

Then its union $\bigcup x$ is also a set.