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Definition df-iun 3971
 Description: Define indexed union. Definition indexed union in [Stoll] p. 45. In most applications, is independent of (although this is not required by the definition), and depends on i.e. can be read informally as . We call the index, the index set, and the indexed set. In most books, is written as a subscript or underneath a union symbol . We use a special union symbol to make it easier to distinguish from plain class union. In many theorems, you will see that and are in the same distinct variable group (meaning cannot depend on ) and that and do not share a distinct variable group (meaning that can be thought of as i.e. can be substituted with a class expression containing ). An alternate definition tying indexed union to ordinary union is dfiun2 4001. Theorem uniiun 4019 provides a definition of ordinary union in terms of indexed union. Theorems fniunfv 5466 and funiunfv 5467 are useful when is a function. (Contributed by NM, 27-Jun-1998.)
Assertion
Ref Expression
df-iun
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Detailed syntax breakdown of Definition df-iun
StepHypRef Expression
1 vx . . 3
2 cA . . 3
3 cB . . 3
41, 2, 3ciun 3969 . 2
5 vy . . . . . 6
65cv 1641 . . . . 5
76, 3wcel 1710 . . . 4
87, 1, 2wrex 2615 . . 3
98, 5cab 2339 . 2
104, 9wceq 1642 1
 Colors of variables: wff setvar class This definition is referenced by:  eliun  3973  nfiun  3995  nfiu1  3997  cbviun  4003  iunss  4007  uniiun  4019  opeliunxp  4820  iunfopab  5204
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