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Theorem bdcpr 15081
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 15080 . . 3 BOUNDED {𝑥}
2 bdcsn 15080 . . 3 BOUNDED {𝑦}
31, 2bdcun 15072 . 2 BOUNDED ({𝑥} ∪ {𝑦})
4 df-pr 3614 . 2 {𝑥, 𝑦} = ({𝑥} ∪ {𝑦})
53, 4bdceqir 15054 1 BOUNDED {𝑥, 𝑦}
Colors of variables: wff set class
Syntax hints:  cun 3142  {csn 3607  {cpr 3608  BOUNDED wbdc 15050
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2171  ax-bd0 15023  ax-bdor 15026  ax-bdeq 15030  ax-bdsb 15032
This theorem depends on definitions:  df-bi 117  df-clab 2176  df-cleq 2182  df-clel 2185  df-un 3148  df-sn 3613  df-pr 3614  df-bdc 15051
This theorem is referenced by:  bdctp  15082  bdop  15085
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