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Definition df-iun 3805
 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 3835. Theorem uniiun 3853 provides a definition of ordinary union in terms of indexed union. Theorems fniunfv 5625 and funiunfv 5626 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 3803 . 2
5 vy . . . . . 6
65cv 1618 . . . . 5
76, 3wcel 1621 . . . 4
87, 1, 2wrex 2510 . . 3
98, 5cab 2239 . 2
104, 9wceq 1619 1
 Colors of variables: wff set class This definition is referenced by:  eliun  3807  nfiun  3829  nfiu1  3831  cbviun  3837  iunss  3841  uniiun  3853  iunopab  4189  opeliunxp  4647  reliun  4713  fnasrn  5554  abrexex2g  5620  abrexex2  5632  marypha2lem4  7075  prismorcsetlem  25078  prismorcset  25080  dfiunv2  25082  bnj956  27497  bnj1143  27511  bnj1146  27512  bnj1400  27557  bnj882  27647  bnj18eq1  27648  bnj893  27649  bnj1398  27753
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