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Definition df-iun 3686
 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 3718. Theorem uniiun 3737 provides a definition of ordinary union in terms of indexed union. (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 3684 . 2
5 vy . . . . . 6
65cv 1258 . . . . 5
76, 3wcel 1409 . . . 4
87, 1, 2wrex 2324 . . 3
98, 5cab 2042 . 2
104, 9wceq 1259 1
 Colors of variables: wff set class This definition is referenced by:  eliun  3688  nfiunxy  3710  nfiunya  3712  nfiu1  3714  dfiunv2  3720  cbviun  3721  iunss  3725  uniiun  3737  iunopab  4045  opeliunxp  4422  reliun  4485  fnasrn  5368  fnasrng  5370  abrexex2g  5774  abrexex2  5778  bdciun  10364
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