Theorem bdcpr 14483

Description: The pair of two setvars is bounded. (Contributed by BJ, 16-Oct-2019.)

Assertion

Ref	Expression
bdcpr	|- BOUNDED { x , y }

Proof of Theorem bdcpr

Step	Hyp	Ref	Expression
1		bdcsn 14482	. . 3 |- BOUNDED { x }
2		bdcsn 14482	. . 3 |- BOUNDED { y }
3	1, 2	bdcun 14474	. 2 |- BOUNDED ( { x } u. { y } )
4		df-pr 3599	. 2 |- { x , y } = ( { x } u. { y } )
5	3, 4	bdceqir 14456	1 |- BOUNDED { x , y }

Syntax hints:   u. cun 3127   {csn 3592   {cpr 3593  BOUNDED wbdc 14452

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14425  ax-bdor 14428  ax-bdeq 14432  ax-bdsb 14434

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-un 3133  df-sn 3598  df-pr 3599  df-bdc 14453

This theorem is referenced by:  bdctp  14484  bdop  14487