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Theorem bdcin 9318
Description: The intersection of two bounded classes is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bdcdif.1 BOUNDED
bdcdif.2 BOUNDED
Assertion
Ref Expression
bdcin BOUNDED  i^i

Proof of Theorem bdcin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcdif.1 . . . . 5 BOUNDED
21bdeli 9301 . . . 4 BOUNDED
3 bdcdif.2 . . . . 5 BOUNDED
43bdeli 9301 . . . 4 BOUNDED
52, 4ax-bdan 9270 . . 3 BOUNDED
65bdcab 9304 . 2 BOUNDED  {  |  }
7 df-in 2918 . 2  i^i  {  |  }
86, 7bdceqir 9299 1 BOUNDED  i^i
Colors of variables: wff set class
Syntax hints:   wa 97   wcel 1390   {cab 2023    i^i cin 2910  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-bdan 9270  ax-bdsb 9277
This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-bdc 9296
This theorem is referenced by: (None)
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