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Theorem bdciin 9999
 Description: The indexed intersection 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
Assertion
Ref Expression
bdciin BOUNDED
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bdciin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdciun.1 . . . . 5 BOUNDED
21bdeli 9966 . . . 4 BOUNDED
32ax-bdal 9938 . . 3 BOUNDED
43bdcab 9969 . 2 BOUNDED
5 df-iin 3660 . 2
64, 5bdceqir 9964 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wcel 1393  cab 2026  wral 2306  ciin 3658  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-bdal 9938  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-iin 3660  df-bdc 9961 This theorem is referenced by: (None)
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