Theorem bdcsuc 13249

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 13217	. . 3 |- BOUNDED x
2		bdcsn 13239	. . 3 |- BOUNDED { x }
3	1, 2	bdcun 13231	. 2 |- BOUNDED ( x u. { x } )
4		df-suc 4301	. 2 |- suc x = ( x u. { x } )
5	3, 4	bdceqir 13213	1 |- BOUNDED suc x

Syntax hints:   u. cun 3074   {csn 3532   suc csuc 4295  BOUNDED wbdc 13209

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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515  ax-ext 2122  ax-bd0 13182  ax-bdor 13185  ax-bdeq 13189  ax-bdel 13190  ax-bdsb 13191

This theorem depends on definitions:  df-bi 116  df-clab 2127  df-cleq 2133  df-clel 2136  df-un 3080  df-sn 3538  df-suc 4301  df-bdc 13210

This theorem is referenced by:  bdeqsuc  13250