Theorem bdctp 9327

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 9326	. . 3 |- BOUNDED {x , y }
2		bdcsn 9325	. . 3 |- BOUNDED {z }
3	1, 2	bdcun 9317	. 2 |- BOUNDED ( {x , y } u. {z })
4		df-tp 3375	. 2 |- {x , y , z } = ( {x , y } u. {z })
5	3, 4	bdceqir 9299	1 |- BOUNDED {x , y , z }

Syntax hints:   u. cun 2909   {csn 3367   {cpr 3368   {ctp 3369  BOUNDED wbdc 9295

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-bd0 9268  ax-bdor 9271  ax-bdeq 9275  ax-bdsb 9277

This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-un 2916  df-sn 3373  df-pr 3374  df-tp 3375  df-bdc 9296

This theorem is referenced by: (None)