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Theorem bdctp 11420
Description: The unordered triple of three setvars is bounded. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdctp BOUNDED {𝑥, 𝑦, 𝑧}

Proof of Theorem bdctp
StepHypRef Expression
1 bdcpr 11419 . . 3 BOUNDED {𝑥, 𝑦}
2 bdcsn 11418 . . 3 BOUNDED {𝑧}
31, 2bdcun 11410 . 2 BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4 df-tp 3449 . 2 {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
53, 4bdceqir 11392 1 BOUNDED {𝑥, 𝑦, 𝑧}
Colors of variables: wff set class
Syntax hints:  cun 2995  {csn 3441  {cpr 3442  {ctp 3443  BOUNDED wbdc 11388
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 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-ext 2070  ax-bd0 11361  ax-bdor 11364  ax-bdeq 11368  ax-bdsb 11370
This theorem depends on definitions:  df-bi 115  df-clab 2075  df-cleq 2081  df-clel 2084  df-un 3001  df-sn 3447  df-pr 3448  df-tp 3449  df-bdc 11389
This theorem is referenced by: (None)
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