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Axiomatic Wiki

WAUnion

Axiom·A03

The union of any family of sets is a set.

The set is the union of D004.
In words
For any family ℱ, there is a set U where for every x, x belongs to U exactly when there is some set A with A in the family and x in A.
This is a ZFC axiom: it is assumed, not proven. Everything below it in a proof chain ultimately rests here.

Remarks

Guarantees the union of D004 exists for every family . Binary union follows by Pairing: .
Wikipedia ↗Set.sUnion ↗

Used by

T17T37T38
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