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Theorem bdcint 9332
 Description: The intersection of a setvar is a bounded class. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdcint BOUNDED x

Proof of Theorem bdcint
Dummy variables y z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ax-bdel 9276 . . . . 5 BOUNDED y z
21ax-bdal 9273 . . . 4 BOUNDED z x y z
3 df-ral 2305 . . . 4 (z x y zz(z xy z))
42, 3bd0 9279 . . 3 BOUNDED z(z xy z)
54bdcab 9304 . 2 BOUNDED {yz(z xy z)}
6 df-int 3607 . 2 x = {yz(z xy z)}
75, 6bdceqir 9299 1 BOUNDED x
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240  {cab 2023  ∀wral 2300  ∩ cint 3606  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-bdal 9273  ax-bdel 9276  ax-bdsb 9277 This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-int 3607  df-bdc 9296 This theorem is referenced by: (None)
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