Theorem bdctp 13241

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 13240	. . 3 |- BOUNDED { x , y }
2		bdcsn 13239	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 13231	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3540	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 13213	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3074   {csn 3532   {cpr 3533   {ctp 3534  BOUNDED wbdc 13209

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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515  ax-ext 2122  ax-bd0 13182  ax-bdor 13185  ax-bdeq 13189  ax-bdsb 13191

This theorem depends on definitions:  df-bi 116  df-clab 2127  df-cleq 2133  df-clel 2136  df-un 3080  df-sn 3538  df-pr 3539  df-tp 3540  df-bdc 13210

This theorem is referenced by: (None)