Theorem bdcsuc 11726

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 11694	. . 3 |- BOUNDED x
2		bdcsn 11716	. . 3 |- BOUNDED { x }
3	1, 2	bdcun 11708	. 2 |- BOUNDED ( x u. { x } )
4		df-suc 4198	. 2 |- suc x = ( x u. { x } )
5	3, 4	bdceqir 11690	1 |- BOUNDED suc x

Syntax hints:   u. cun 2997   {csn 3446   suc csuc 4192  BOUNDED wbdc 11686

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-ext 2070  ax-bd0 11659  ax-bdor 11662  ax-bdeq 11666  ax-bdel 11667  ax-bdsb 11668

This theorem depends on definitions:  df-bi 115  df-clab 2075  df-cleq 2081  df-clel 2084  df-un 3003  df-sn 3452  df-suc 4198  df-bdc 11687

This theorem is referenced by:  bdeqsuc  11727