Theorem bdcsuc 16535

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 16503	. . 3 |- BOUNDED x
2		bdcsn 16525	. . 3 |- BOUNDED { x }
3	1, 2	bdcun 16517	. 2 |- BOUNDED ( x u. { x } )
4		df-suc 4470	. 2 |- suc x = ( x u. { x } )
5	3, 4	bdceqir 16499	1 |- BOUNDED suc x

Syntax hints:   u. cun 3197   {csn 3670   suc csuc 4464  BOUNDED wbdc 16495

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582  ax-ext 2212  ax-bd0 16468  ax-bdor 16471  ax-bdeq 16475  ax-bdel 16476  ax-bdsb 16477

This theorem depends on definitions:  df-bi 117  df-clab 2217  df-cleq 2223  df-clel 2226  df-un 3203  df-sn 3676  df-suc 4470  df-bdc 16496

This theorem is referenced by:  bdeqsuc  16536