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Theorem bdctp 11120
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 11119 . . 3 BOUNDED {𝑥, 𝑦}
2 bdcsn 11118 . . 3 BOUNDED {𝑧}
31, 2bdcun 11110 . 2 BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4 df-tp 3433 . 2 {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
53, 4bdceqir 11092 1 BOUNDED {𝑥, 𝑦, 𝑧}
Colors of variables: wff set class
Syntax hints:  cun 2984  {csn 3425  {cpr 3426  {ctp 3427  BOUNDED wbdc 11088
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 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470  ax-ext 2067  ax-bd0 11061  ax-bdor 11064  ax-bdeq 11068  ax-bdsb 11070
This theorem depends on definitions:  df-bi 115  df-clab 2072  df-cleq 2078  df-clel 2081  df-un 2990  df-sn 3431  df-pr 3432  df-tp 3433  df-bdc 11089
This theorem is referenced by: (None)
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