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Theorem bdctp 12904
Description: The unordered triple of three setvars is bounded. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdctp  |- BOUNDED  { x ,  y ,  z }

Proof of Theorem bdctp
StepHypRef Expression
1 bdcpr 12903 . . 3  |- BOUNDED  { x ,  y }
2 bdcsn 12902 . . 3  |- BOUNDED  { z }
31, 2bdcun 12894 . 2  |- BOUNDED  ( { x ,  y }  u.  {
z } )
4 df-tp 3503 . 2  |-  { x ,  y ,  z }  =  ( { x ,  y }  u.  { z } )
53, 4bdceqir 12876 1  |- BOUNDED  { x ,  y ,  z }
Colors of variables: wff set class
Syntax hints:    u. cun 3037   {csn 3495   {cpr 3496   {ctp 3497  BOUNDED wbdc 12872
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 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-17 1489  ax-ial 1497  ax-ext 2097  ax-bd0 12845  ax-bdor 12848  ax-bdeq 12852  ax-bdsb 12854
This theorem depends on definitions:  df-bi 116  df-clab 2102  df-cleq 2108  df-clel 2111  df-un 3043  df-sn 3501  df-pr 3502  df-tp 3503  df-bdc 12873
This theorem is referenced by: (None)
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