Theorem bdctp 13385

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 13384	. . 3 |- BOUNDED { x , y }
2		bdcsn 13383	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 13375	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3564	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 13357	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3096   {csn 3556   {cpr 3557   {ctp 3558  BOUNDED wbdc 13353

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 1487  ax-17 1503  ax-ial 1511  ax-ext 2136  ax-bd0 13326  ax-bdor 13329  ax-bdeq 13333  ax-bdsb 13335

This theorem depends on definitions:  df-bi 116  df-clab 2141  df-cleq 2147  df-clel 2150  df-un 3102  df-sn 3562  df-pr 3563  df-tp 3564  df-bdc 13354

This theorem is referenced by: (None)