Theorem bdcsuc 13772

Description: The successor of a setvar is a bounded class. (Contributed by BJ, 16-Oct-2019.)

Assertion

Ref	Expression
bdcsuc	|- BOUNDED suc x

Proof of Theorem bdcsuc

Step	Hyp	Ref	Expression
1		bdcv 13740	. . 3 |- BOUNDED x
2		bdcsn 13762	. . 3 |- BOUNDED { x }
3	1, 2	bdcun 13754	. 2 |- BOUNDED ( x u. { x } )
4		df-suc 4349	. 2 |- suc x = ( x u. { x } )
5	3, 4	bdceqir 13736	1 |- BOUNDED suc x

Syntax hints:   u. cun 3114   {csn 3576   suc csuc 4343  BOUNDED wbdc 13732

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-17 1514  ax-ial 1522  ax-ext 2147  ax-bd0 13705  ax-bdor 13708  ax-bdeq 13712  ax-bdel 13713  ax-bdsb 13714

This theorem depends on definitions:  df-bi 116  df-clab 2152  df-cleq 2158  df-clel 2161  df-un 3120  df-sn 3582  df-suc 4349  df-bdc 13733

This theorem is referenced by:  bdeqsuc  13773