Theorem bdcpr 11105

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 11104	. . 3 |- BOUNDED { x }
2		bdcsn 11104	. . 3 |- BOUNDED { y }
3	1, 2	bdcun 11096	. 2 |- BOUNDED ( { x } u. { y } )
4		df-pr 3429	. 2 |- { x , y } = ( { x } u. { y } )
5	3, 4	bdceqir 11078	1 |- BOUNDED { x , y }

Syntax hints:   u. cun 2982   {csn 3422   {cpr 3423  BOUNDED wbdc 11074

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2065  ax-bd0 11047  ax-bdor 11050  ax-bdeq 11054  ax-bdsb 11056

This theorem depends on definitions:  df-bi 115  df-clab 2070  df-cleq 2076  df-clel 2079  df-un 2988  df-sn 3428  df-pr 3429  df-bdc 11075

This theorem is referenced by:  bdctp  11106  bdop  11109