Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdctp GIF version

Theorem bdctp 15102
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 15101 . . 3 BOUNDED {𝑥, 𝑦}
2 bdcsn 15100 . . 3 BOUNDED {𝑧}
31, 2bdcun 15092 . 2 BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4 df-tp 3615 . 2 {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
53, 4bdceqir 15074 1 BOUNDED {𝑥, 𝑦, 𝑧}
Colors of variables: wff set class
Syntax hints:  cun 3142  {csn 3607  {cpr 3608  {ctp 3609  BOUNDED wbdc 15070
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 15043  ax-bdor 15046  ax-bdeq 15050  ax-bdsb 15052
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-tp 3615  df-bdc 15071
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator