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Theorem bdcin 9983
 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

Proof of Theorem bdcin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcdif.1 . . . . 5 BOUNDED
21bdeli 9966 . . . 4 BOUNDED
3 bdcdif.2 . . . . 5 BOUNDED
43bdeli 9966 . . . 4 BOUNDED
52, 4ax-bdan 9935 . . 3 BOUNDED
65bdcab 9969 . 2 BOUNDED
7 df-in 2924 . 2
86, 7bdceqir 9964 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wa 97   wcel 1393  cab 2026   cin 2916  BOUNDED wbdc 9960 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-bd0 9933  ax-bdan 9935  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-bdc 9961 This theorem is referenced by: (None)
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