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Theorem bdcpr 12996
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 12995 . . 3  |- BOUNDED  { x }
2 bdcsn 12995 . . 3  |- BOUNDED  { y }
31, 2bdcun 12987 . 2  |- BOUNDED  ( { x }  u.  { y } )
4 df-pr 3504 . 2  |-  { x ,  y }  =  ( { x }  u.  { y } )
53, 4bdceqir 12969 1  |- BOUNDED  { x ,  y }
Colors of variables: wff set class
Syntax hints:    u. cun 3039   {csn 3497   {cpr 3498  BOUNDED wbdc 12965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-17 1491  ax-ial 1499  ax-ext 2099  ax-bd0 12938  ax-bdor 12941  ax-bdeq 12945  ax-bdsb 12947
This theorem depends on definitions:  df-bi 116  df-clab 2104  df-cleq 2110  df-clel 2113  df-un 3045  df-sn 3503  df-pr 3504  df-bdc 12966
This theorem is referenced by:  bdctp  12997  bdop  13000
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