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Theorem bdctp 14506
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 14505 . . 3  |- BOUNDED  { x ,  y }
2 bdcsn 14504 . . 3  |- BOUNDED  { z }
31, 2bdcun 14496 . 2  |- BOUNDED  ( { x ,  y }  u.  {
z } )
4 df-tp 3600 . 2  |-  { x ,  y ,  z }  =  ( { x ,  y }  u.  { z } )
53, 4bdceqir 14478 1  |- BOUNDED  { x ,  y ,  z }
Colors of variables: wff set class
Syntax hints:    u. cun 3127   {csn 3592   {cpr 3593   {ctp 3594  BOUNDED wbdc 14474
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 14447  ax-bdor 14450  ax-bdeq 14454  ax-bdsb 14456
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-tp 3600  df-bdc 14475
This theorem is referenced by: (None)
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