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Theorem bdctp 15770
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 15769 . . 3  |- BOUNDED  { x ,  y }
2 bdcsn 15768 . . 3  |- BOUNDED  { z }
31, 2bdcun 15760 . 2  |- BOUNDED  ( { x ,  y }  u.  {
z } )
4 df-tp 3640 . 2  |-  { x ,  y ,  z }  =  ( { x ,  y }  u.  { z } )
53, 4bdceqir 15742 1  |- BOUNDED  { x ,  y ,  z }
Colors of variables: wff set class
Syntax hints:    u. cun 3163   {csn 3632   {cpr 3633   {ctp 3634  BOUNDED wbdc 15738
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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-17 1548  ax-ial 1556  ax-ext 2186  ax-bd0 15711  ax-bdor 15714  ax-bdeq 15718  ax-bdsb 15720
This theorem depends on definitions:  df-bi 117  df-clab 2191  df-cleq 2197  df-clel 2200  df-un 3169  df-sn 3638  df-pr 3639  df-tp 3640  df-bdc 15739
This theorem is referenced by: (None)
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