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Theorem bdctp 15309
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 15308 . . 3 BOUNDED {𝑥, 𝑦}
2 bdcsn 15307 . . 3 BOUNDED {𝑧}
31, 2bdcun 15299 . 2 BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4 df-tp 3626 . 2 {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
53, 4bdceqir 15281 1 BOUNDED {𝑥, 𝑦, 𝑧}
Colors of variables: wff set class
Syntax hints:  cun 3151  {csn 3618  {cpr 3619  {ctp 3620  BOUNDED wbdc 15277
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 2175  ax-bd0 15250  ax-bdor 15253  ax-bdeq 15257  ax-bdsb 15259
This theorem depends on definitions:  df-bi 117  df-clab 2180  df-cleq 2186  df-clel 2189  df-un 3157  df-sn 3624  df-pr 3625  df-tp 3626  df-bdc 15278
This theorem is referenced by: (None)
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