Axiom 3.11 (Union). Let \(A\) be a set, all of whose elements are themselves sets. Then there exists a set \(\bigcup A\) whose elements are precisely those objects which are elements of the elements of \(A\), thus for all objects \(x\) $$ x\in\bigcup A\iff(x\in S\text{ for some }S\in A) $$
Axiom 3.11
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Exercise 3.4.8
\(\vdash\) { Axiom 3.11 }