Theorem bdcsuc 16699

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 16667	. . 3 |- BOUNDED x
2		bdcsn 16689	. . 3 |- BOUNDED { x }
3	1, 2	bdcun 16681	. 2 |- BOUNDED ( x u. { x } )
4		df-suc 4494	. 2 |- suc x = ( x u. { x } )
5	3, 4	bdceqir 16663	1 |- BOUNDED suc x

Syntax hints:   u. cun 3211   {csn 3691   suc csuc 4488  BOUNDED wbdc 16659

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2216  ax-bd0 16632  ax-bdor 16635  ax-bdeq 16639  ax-bdel 16640  ax-bdsb 16641

This theorem depends on definitions:  df-bi 117  df-clab 2221  df-cleq 2227  df-clel 2230  df-un 3217  df-sn 3697  df-suc 4494  df-bdc 16660

This theorem is referenced by:  bdeqsuc  16700