Theorem bdctp 15808

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 15807	. . 3 |- BOUNDED { x , y }
2		bdcsn 15806	. . 3 |- BOUNDED { z }
3	1, 2	bdcun 15798	. 2 |- BOUNDED ( { x , y } u. { z } )
4		df-tp 3641	. 2 |- { x , y , z } = ( { x , y } u. { z } )
5	3, 4	bdceqir 15780	1 |- BOUNDED { x , y , z }

Syntax hints:   u. cun 3164   {csn 3633   {cpr 3634   {ctp 3635  BOUNDED wbdc 15776

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557  ax-ext 2187  ax-bd0 15749  ax-bdor 15752  ax-bdeq 15756  ax-bdsb 15758

This theorem depends on definitions:  df-bi 117  df-clab 2192  df-cleq 2198  df-clel 2201  df-un 3170  df-sn 3639  df-pr 3640  df-tp 3641  df-bdc 15777

This theorem is referenced by: (None)