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Theorem bdcpr 10913
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 10912 . . 3 BOUNDED {𝑥}
2 bdcsn 10912 . . 3 BOUNDED {𝑦}
31, 2bdcun 10904 . 2 BOUNDED ({𝑥} ∪ {𝑦})
4 df-pr 3424 . 2 {𝑥, 𝑦} = ({𝑥} ∪ {𝑦})
53, 4bdceqir 10886 1 BOUNDED {𝑥, 𝑦}
Colors of variables: wff set class
Syntax hints:  cun 2981  {csn 3417  {cpr 3418  BOUNDED wbdc 10882
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2065  ax-bd0 10855  ax-bdor 10858  ax-bdeq 10862  ax-bdsb 10864
This theorem depends on definitions:  df-bi 115  df-clab 2070  df-cleq 2076  df-clel 2079  df-un 2987  df-sn 3423  df-pr 3424  df-bdc 10883
This theorem is referenced by:  bdctp  10914  bdop  10917
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