Theorem bdctp 16007

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 16006	. . 3 |- BOUNDED { x , y }
2		bdcsn 16005	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 15997	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3651	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 15979	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3172   {csn 3643   {cpr 3644   {ctp 3645  BOUNDED wbdc 15975

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558  ax-ext 2189  ax-bd0 15948  ax-bdor 15951  ax-bdeq 15955  ax-bdsb 15957

This theorem depends on definitions:  df-bi 117  df-clab 2194  df-cleq 2200  df-clel 2203  df-un 3178  df-sn 3649  df-pr 3650  df-tp 3651  df-bdc 15976

This theorem is referenced by: (None)