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Definition df-iun 3629
Description: Define indexed union. Definition indexed union in [Stoll] p. 45. In most applications, A is independent of x (although this is not required by the definition), and B depends on x i.e. can be read informally as B(x). We call x the index, A the index set, and B the indexed set. In most books, x A 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 x and A are in the same distinct variable group (meaning A cannot depend on x) and that B and x do not share a distinct variable group (meaning that can be thought of as B(x) i.e. can be substituted with a class expression containing x). An alternate definition tying indexed union to ordinary union is dfiun2 3661. Theorem uniiun 3680 provides a definition of ordinary union in terms of indexed union. (Contributed by NM, 27-Jun-1998.)
Assertion
Ref Expression
df-iun x A B = {yx A y B}
Distinct variable groups:   x,y   y,A   y,B
Allowed substitution hints:   A(x)   B(x)

Detailed syntax breakdown of Definition df-iun
StepHypRef Expression
1 vx . . 3 setvar x
2 cA . . 3 class A
3 cB . . 3 class B
41, 2, 3ciun 3627 . 2 class x A B
5 vy . . . . . 6 setvar y
65cv 1225 . . . . 5 class y
76, 3wcel 1370 . . . 4 wff y B
87, 1, 2wrex 2281 . . 3 wff x A y B
98, 5cab 2004 . 2 class {yx A y B}
104, 9wceq 1226 1 wff x A B = {yx A y B}
Colors of variables: wff set class
This definition is referenced by:  eliun  3631  nfiunxy  3653  nfiunya  3655  nfiu1  3657  dfiunv2  3663  cbviun  3664  iunss  3668  uniiun  3680  iunopab  3988  opeliunxp  4318  reliun  4381  fnasrn  5262  fnasrng  5264  abrexex2g  5666  abrexex2  5670  bdciun  7244
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