Theorem bdctp 16470

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 16469	. . 3 |- BOUNDED { x , y }
2		bdcsn 16468	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 16460	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3677	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 16442	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3198   {csn 3669   {cpr 3670   {ctp 3671  BOUNDED wbdc 16438

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582  ax-ext 2213  ax-bd0 16411  ax-bdor 16414  ax-bdeq 16418  ax-bdsb 16420

This theorem depends on definitions:  df-bi 117  df-clab 2218  df-cleq 2224  df-clel 2227  df-un 3204  df-sn 3675  df-pr 3676  df-tp 3677  df-bdc 16439

This theorem is referenced by: (None)