Theorem bdctp 16629

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 16628	. . 3 |- BOUNDED { x , y }
2		bdcsn 16627	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 16619	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3696	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 16601	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3208   {csn 3688   {cpr 3689   {ctp 3690  BOUNDED wbdc 16597

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2214  ax-bd0 16570  ax-bdor 16573  ax-bdeq 16577  ax-bdsb 16579

This theorem depends on definitions:  df-bi 117  df-clab 2219  df-cleq 2225  df-clel 2228  df-un 3214  df-sn 3694  df-pr 3695  df-tp 3696  df-bdc 16598

This theorem is referenced by: (None)