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Theorem bdcpr 9434
Description: The pair of two setvars is bounded. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdcpr BOUNDED  { ,  }

Proof of Theorem bdcpr
StepHypRef Expression
1 bdcsn 9433 . . 3 BOUNDED  { }
2 bdcsn 9433 . . 3 BOUNDED  { }
31, 2bdcun 9425 . 2 BOUNDED  { }  u.  { }
4 df-pr 3377 . 2  { ,  }  { }  u.  { }
53, 4bdceqir 9407 1 BOUNDED  { ,  }
Colors of variables: wff set class
Syntax hints:    u. cun 2912   {csn 3370   {cpr 3371  BOUNDED wbdc 9403
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 9376  ax-bdor 9379  ax-bdeq 9383  ax-bdsb 9385
This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-un 2919  df-sn 3376  df-pr 3377  df-bdc 9404
This theorem is referenced by:  bdctp  9435  bdop  9438
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