Theorem bdctp 16235

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

Step	Hyp	Ref	Expression
1		bdcpr 16234	. . 3 |- BOUNDED { x , y }
2		bdcsn 16233	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 16225	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3674	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 16207	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3195   {csn 3666   {cpr 3667   {ctp 3668  BOUNDED wbdc 16203

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-bd0 16176  ax-bdor 16179  ax-bdeq 16183  ax-bdsb 16185

This theorem depends on definitions:  df-bi 117  df-clab 2216  df-cleq 2222  df-clel 2225  df-un 3201  df-sn 3672  df-pr 3673  df-tp 3674  df-bdc 16204

This theorem is referenced by: (None)