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Theorem bdcpr 11105
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 11104 . . 3  |- BOUNDED  { x }
2 bdcsn 11104 . . 3  |- BOUNDED  { y }
31, 2bdcun 11096 . 2  |- BOUNDED  ( { x }  u.  { y } )
4 df-pr 3429 . 2  |-  { x ,  y }  =  ( { x }  u.  { y } )
53, 4bdceqir 11078 1  |- BOUNDED  { x ,  y }
Colors of variables: wff set class
Syntax hints:    u. cun 2982   {csn 3422   {cpr 3423  BOUNDED wbdc 11074
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2065  ax-bd0 11047  ax-bdor 11050  ax-bdeq 11054  ax-bdsb 11056
This theorem depends on definitions:  df-bi 115  df-clab 2070  df-cleq 2076  df-clel 2079  df-un 2988  df-sn 3428  df-pr 3429  df-bdc 11075
This theorem is referenced by:  bdctp  11106  bdop  11109
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