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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 }  u.  { y } )
4 df-pr 3448 . 2  |-  { x ,  y }  =  ( { x }  u.  { y } )
53, 4bdceqir 11381 1  |- BOUNDED  { x ,  y }
Colors of variables: wff set class
Syntax hints:    u. 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
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