Theorem bdcsuc 14492

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 14460	. . 3 |- BOUNDED x
2		bdcsn 14482	. . 3 |- BOUNDED { x }
3	1, 2	bdcun 14474	. 2 |- BOUNDED ( x u. { x } )
4		df-suc 4370	. 2 |- suc x = ( x u. { x } )
5	3, 4	bdceqir 14456	1 |- BOUNDED suc x

Syntax hints:   u. cun 3127   {csn 3592   suc csuc 4364  BOUNDED wbdc 14452

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14425  ax-bdor 14428  ax-bdeq 14432  ax-bdel 14433  ax-bdsb 14434

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-un 3133  df-sn 3598  df-suc 4370  df-bdc 14453

This theorem is referenced by:  bdeqsuc  14493