 Axiom of union

For every set $x$, there is a set $u=\bigcup x$ whose elements are exactly the elements of members of $x$:

The Axiom of Union is one of the axioms in set theory, particularly within the Zermelo-Fraenkel set theory (ZF), which is a foundational system for mathematics. The Axiom of Union states that for any set \( A \), there exists a set \( B \) that contains exactly the elements of the elements of \( A \).