Theorem bdcpr 15363

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 15362	. . 3 |- BOUNDED { x }
2		bdcsn 15362	. . 3 |- BOUNDED { y }
3	1, 2	bdcun 15354	. 2 |- BOUNDED ( { x } u. { y } )
4		df-pr 3625	. 2 |- { x , y } = ( { x } u. { y } )
5	3, 4	bdceqir 15336	1 |- BOUNDED { x , y }

Syntax hints:   u. cun 3151   {csn 3618   {cpr 3619  BOUNDED wbdc 15332

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-bd0 15305  ax-bdor 15308  ax-bdeq 15312  ax-bdsb 15314

This theorem depends on definitions:  df-bi 117  df-clab 2180  df-cleq 2186  df-clel 2189  df-un 3157  df-sn 3624  df-pr 3625  df-bdc 15333

This theorem is referenced by:  bdctp  15364  bdop  15367