Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdciun Structured version   GIF version

Theorem bdciun 9333
 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 9301 . . . 4 BOUNDED z A
32ax-bdex 9274 . . 3 BOUNDED x y z A
43bdcab 9304 . 2 BOUNDED {zx y z A}
5 df-iun 3650 . 2 x y A = {zx y z A}
64, 5bdceqir 9299 1 BOUNDED x y A
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1390  {cab 2023  ∃wrex 2301  ∪ ciun 3648  BOUNDED wbdc 9295 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 9268  ax-bdex 9274  ax-bdsb 9277 This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-iun 3650  df-bdc 9296 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator