ax-un - Metamath Proof Explorer

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Axiom ax-un 7727
Description: Axiom of Union. An axiom of Zermelo-Fraenkel set theory. It states that a set exists that includes the union of a given set i.e. the collection of all members of the members of . The variant axun2 7729 states that the union itself exists. A version with the standard abbreviation for union is uniex2 7730. A version using class notation is uniex 7733.

The union of a class df-uni 4884 should not be confused with the union of two classes df-un 3931. Their relationship is shown in unipr 4900. (Contributed by NM, 23-Dec-1993.)

Assertion
Ref Expression
ax-un
Distinct variable group: ,,,

Detailed syntax breakdown of Axiom ax-un
StepHypRef Expression
1vz . . . . . . 7
2vw . . . . . . 7
31, 2wel 2109 . . . . . 6
4vx . . . . . . 7
52, 4wel 2109 . . . . . 6
63, 5wa 395 . . . . 5
76, 2wex 1779 . . . 4
8vy . . . . 5
91, 8wel 2109 . . . 4
107, 9wi 4 . . 3
1110, 1wal 1538 . 2
1211, 8wex 1779 1
Colors of variables: wff setvar class
This axiom is referenced by: zfun 7728 axun2 7729 uniex2 7730
Copyright terms: Public domain W3C validator

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