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Theorem bdcpr 9991
 Description: The pair of two setvars is bounded. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdcpr BOUNDED {𝑥, 𝑦}

Proof of Theorem bdcpr
StepHypRef Expression
1 bdcsn 9990 . . 3 BOUNDED {𝑥}
2 bdcsn 9990 . . 3 BOUNDED {𝑦}
31, 2bdcun 9982 . 2 BOUNDED ({𝑥} ∪ {𝑦})
4 df-pr 3382 . 2 {𝑥, 𝑦} = ({𝑥} ∪ {𝑦})
53, 4bdceqir 9964 1 BOUNDED {𝑥, 𝑦}
 Colors of variables: wff set class Syntax hints:   ∪ cun 2915  {csn 3375  {cpr 3376  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-bdor 9936  ax-bdeq 9940  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-un 2922  df-sn 3381  df-pr 3382  df-bdc 9961 This theorem is referenced by:  bdctp  9992  bdop  9995
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