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Definition df-iun 3622
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 3654. Theorem uniiun 3673 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 3620 . 2 class x A B
5 vy . . . . . 6 setvar y
65cv 1222 . . . . 5 class y
76, 3wcel 1366 . . . 4 wff y B
87, 1, 2wrex 2276 . . 3 wff x A y B
98, 5cab 1999 . 2 class {yx A y B}
104, 9wceq 1223 1 wff x A B = {yx A y B}
Colors of variables: wff set class
This definition is referenced by:  eliun  3624  nfiunxy  3646  nfiunya  3648  nfiu1  3650  dfiunv2  3656  cbviun  3657  iunss  3661  uniiun  3673  iunopab  3981  opeliunxp  4310  reliun  4373  fnasrn  5254  fnasrng  5256  abrexex2g  5658  abrexex2  5662  bdciun  8263
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