MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-un Unicode version

Axiom ax-un 6382
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 6384 states that the union itself exists. A version with the standard abbreviation for union is uniex2 6385. A version using class notation is uniex 6386.

The union of a class df-uni 4118 should not be confused with the union of two classes df-un 3370. Their relationship is shown in unipr 4130. (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 1733 . . . . . 6
4 vx . . . . . . 7
52, 4wel 1733 . . . . . 6
63, 5wa 360 . . . . 5
76, 2wex 1565 . . . 4
8 vy . . . . 5
91, 8wel 1733 . . . 4
107, 9wi 4 . . 3
1110, 1wal 1564 . 2
1211, 8wex 1565 1
Colors of variables: wff set class
This axiom is referenced by:  zfun  6383  axun2  6384
  Copyright terms: Public domain W3C validator