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Theorem bdcpr 14483
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 14482 . . 3  |- BOUNDED  { x }
2 bdcsn 14482 . . 3  |- BOUNDED  { y }
31, 2bdcun 14474 . 2  |- BOUNDED  ( { x }  u.  { y } )
4 df-pr 3599 . 2  |-  { x ,  y }  =  ( { x }  u.  { y } )
53, 4bdceqir 14456 1  |- BOUNDED  { x ,  y }
Colors of variables: wff set class
Syntax hints:    u. cun 3127   {csn 3592   {cpr 3593  BOUNDED wbdc 14452
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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14425  ax-bdor 14428  ax-bdeq 14432  ax-bdsb 14434
This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-un 3133  df-sn 3598  df-pr 3599  df-bdc 14453
This theorem is referenced by:  bdctp  14484  bdop  14487
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