Theorem bdctp 9992

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 9991	. . 3 |- BOUNDED { x , y }
2		bdcsn 9990	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 9982	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3383	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 9964	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 2915   {csn 3375   {cpr 3376   {ctp 3377  BOUNDED wbdc 9960

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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-bd0 9933  ax-bdor 9936  ax-bdeq 9940  ax-bdsb 9942

This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-un 2922  df-sn 3381  df-pr 3382  df-tp 3383  df-bdc 9961

This theorem is referenced by: (None)