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Axiom ax-un 4742
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 4744 states that the union itself exists. A version with the standard abbreviation for union is uniex2 4745. A version using class notation is uniex 4746.

The union of a class df-uni 4044 should not be confused with the union of two classes df-un 3314. Their relationship is shown in unipr 4056. (Contributed by NM, 23-Dec-1993.)

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

Detailed syntax breakdown of Axiom ax-un
StepHypRef Expression
1 vz . . . . . . 7
2 vw . . . . . . 7
31, 2wel 1729 . . . . . 6
4 vx . . . . . . 7
52, 4wel 1729 . . . . . 6
63, 5wa 360 . . . . 5
76, 2wex 1551 . . . 4
8 vy . . . . 5
91, 8wel 1729 . . . 4
107, 9wi 4 . . 3
1110, 1wal 1550 . 2
1211, 8wex 1551 1
Colors of variables: wff set class
This axiom is referenced by:  zfun  4743  axun2  4744
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