Theorem bdctp 15770

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 15769	. . 3 |- BOUNDED { x , y }
2		bdcsn 15768	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 15760	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3640	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 15742	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3163   {csn 3632   {cpr 3633   {ctp 3634  BOUNDED wbdc 15738

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-17 1548  ax-ial 1556  ax-ext 2186  ax-bd0 15711  ax-bdor 15714  ax-bdeq 15718  ax-bdsb 15720

This theorem depends on definitions:  df-bi 117  df-clab 2191  df-cleq 2197  df-clel 2200  df-un 3169  df-sn 3638  df-pr 3639  df-tp 3640  df-bdc 15739

This theorem is referenced by: (None)