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

Theorem bdcpr 11408
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 11407 . . 3 BOUNDED {𝑥}
2 bdcsn 11407 . . 3 BOUNDED {𝑦}
31, 2bdcun 11399 . 2 BOUNDED ({𝑥} ∪ {𝑦})
4 df-pr 3448 . 2 {𝑥, 𝑦} = ({𝑥} ∪ {𝑦})
53, 4bdceqir 11381 1 BOUNDED {𝑥, 𝑦}
Colors of variables: wff set class
Syntax hints:  cun 2995  {csn 3441  {cpr 3442  BOUNDED wbdc 11377
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 11350  ax-bdor 11353  ax-bdeq 11357  ax-bdsb 11359
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-bdc 11378
This theorem is referenced by:  bdctp  11409  bdop  11412
  Copyright terms: Public domain W3C validator