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Definition df-iun 3650
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 3682. Theorem uniiun 3701 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 3648 . 2 class x A B
5 vy . . . . . 6 setvar y
65cv 1241 . . . . 5 class y
76, 3wcel 1390 . . . 4 wff y B
87, 1, 2wrex 2301 . . 3 wff x A y B
98, 5cab 2023 . 2 class {yx A y B}
104, 9wceq 1242 1 wff x A B = {yx A y B}
Colors of variables: wff set class
This definition is referenced by:  eliun  3652  nfiunxy  3674  nfiunya  3676  nfiu1  3678  dfiunv2  3684  cbviun  3685  iunss  3689  uniiun  3701  iunopab  4009  opeliunxp  4338  reliun  4401  fnasrn  5284  fnasrng  5286  abrexex2g  5689  abrexex2  5693  bdciun  9267
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