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Theorem bdciun 9313
Description: The indexed union of a bounded class with a setvar indexing set is a bounded class. (Contributed by BJ, 16-Oct-2019.)
Hypothesis
Ref Expression
bdciun.1 BOUNDED A
Assertion
Ref Expression
bdciun BOUNDED x y A
Distinct variable group:   x,y
Allowed substitution hints:   A(x,y)

Proof of Theorem bdciun
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 bdciun.1 . . . . 5 BOUNDED A
21bdeli 9281 . . . 4 BOUNDED z A
32ax-bdex 9254 . . 3 BOUNDED x y z A
43bdcab 9284 . 2 BOUNDED {zx y z A}
5 df-iun 3650 . 2 x y A = {zx y z A}
64, 5bdceqir 9279 1 BOUNDED x y A
Colors of variables: wff set class
Syntax hints:   wcel 1390  {cab 2023  wrex 2301   ciun 3648  BOUNDED wbdc 9275
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-bd0 9248  ax-bdex 9254  ax-bdsb 9257
This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-iun 3650  df-bdc 9276
This theorem is referenced by: (None)
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