Theorem bdcpr 16402

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 16401	. . 3 |- BOUNDED { x }
2		bdcsn 16401	. . 3 |- BOUNDED { y }
3	1, 2	bdcun 16393	. 2 |- BOUNDED ( { x } u. { y } )
4		df-pr 3674	. 2 |- { x , y } = ( { x } u. { y } )
5	3, 4	bdceqir 16375	1 |- BOUNDED { x , y }

Syntax hints:   u. cun 3196   {csn 3667   {cpr 3668  BOUNDED wbdc 16371

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-bd0 16344  ax-bdor 16347  ax-bdeq 16351  ax-bdsb 16353

This theorem depends on definitions:  df-bi 117  df-clab 2216  df-cleq 2222  df-clel 2225  df-un 3202  df-sn 3673  df-pr 3674  df-bdc 16372

This theorem is referenced by:  bdctp  16403  bdop  16406