Theorem bdcsuc 15634

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 15602	. . 3 |- BOUNDED x
2		bdcsn 15624	. . 3 |- BOUNDED { x }
3	1, 2	bdcun 15616	. 2 |- BOUNDED ( x u. { x } )
4		df-suc 4407	. 2 |- suc x = ( x u. { x } )
5	3, 4	bdceqir 15598	1 |- BOUNDED suc x

Syntax hints:   u. cun 3155   {csn 3623   suc csuc 4401  BOUNDED wbdc 15594

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-bd0 15567  ax-bdor 15570  ax-bdeq 15574  ax-bdel 15575  ax-bdsb 15576

This theorem depends on definitions:  df-bi 117  df-clab 2183  df-cleq 2189  df-clel 2192  df-un 3161  df-sn 3629  df-suc 4407  df-bdc 15595

This theorem is referenced by:  bdeqsuc  15635