Theorem bdctp 13059

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 13058	. . 3 |- BOUNDED { x , y }
2		bdcsn 13057	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 13049	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3530	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 13031	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3064   {csn 3522   {cpr 3523   {ctp 3524  BOUNDED wbdc 13027

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2119  ax-bd0 13000  ax-bdor 13003  ax-bdeq 13007  ax-bdsb 13009

This theorem depends on definitions:  df-bi 116  df-clab 2124  df-cleq 2130  df-clel 2133  df-un 3070  df-sn 3528  df-pr 3529  df-tp 3530  df-bdc 13028

This theorem is referenced by: (None)