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Theorem bdcsuc 11128
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 11096 . . 3  |- BOUNDED  x
2 bdcsn 11118 . . 3  |- BOUNDED  { x }
31, 2bdcun 11110 . 2  |- BOUNDED  ( x  u.  {
x } )
4 df-suc 4165 . 2  |-  suc  x  =  ( x  u. 
{ x } )
53, 4bdceqir 11092 1  |- BOUNDED  suc  x
Colors of variables: wff set class
Syntax hints:    u. cun 2984   {csn 3425   suc csuc 4159  BOUNDED wbdc 11088
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 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470  ax-ext 2067  ax-bd0 11061  ax-bdor 11064  ax-bdeq 11068  ax-bdel 11069  ax-bdsb 11070
This theorem depends on definitions:  df-bi 115  df-clab 2072  df-cleq 2078  df-clel 2081  df-un 2990  df-sn 3431  df-suc 4165  df-bdc 11089
This theorem is referenced by:  bdeqsuc  11129
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