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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
StepHypRef Expression
1 bdcv 11694 . . 3  |- BOUNDED  x
2 bdcsn 11716 . . 3  |- BOUNDED  { x }
31, 2bdcun 11708 . 2  |- BOUNDED  ( x  u.  {
x } )
4 df-suc 4198 . 2  |-  suc  x  =  ( x  u. 
{ x } )
53, 4bdceqir 11690 1  |- BOUNDED  suc  x
Colors of variables: wff set class
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
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