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Theorem bdcsuc 9315
 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 9283 . . 3 BOUNDED x
2 bdcsn 9305 . . 3 BOUNDED {x}
31, 2bdcun 9297 . 2 BOUNDED (x ∪ {x})
4 df-suc 4074 . 2 suc x = (x ∪ {x})
53, 4bdceqir 9279 1 BOUNDED suc x
 Colors of variables: wff set class Syntax hints:   ∪ cun 2909  {csn 3367  suc csuc 4068  BOUNDED wbdc 9275 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-bd0 9248  ax-bdor 9251  ax-bdeq 9255  ax-bdel 9256  ax-bdsb 9257 This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-un 2916  df-sn 3373  df-suc 4074  df-bdc 9276 This theorem is referenced by:  bdeqsuc  9316
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