Theorem bdctp 16881

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 16880	. . 3 |- BOUNDED { x , y }
2		bdcsn 16879	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 16871	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3716	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 16853	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3218   {csn 3708   {cpr 3709   {ctp 3710  BOUNDED wbdc 16849

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-bd0 16822  ax-bdor 16825  ax-bdeq 16829  ax-bdsb 16831

This theorem depends on definitions:  df-bi 117  df-clab 2225  df-cleq 2231  df-clel 2234  df-un 3224  df-sn 3714  df-pr 3715  df-tp 3716  df-bdc 16850

This theorem is referenced by: (None)