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Theorem bdcsuc 13393
 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 13361 . . 3 BOUNDED 𝑥
2 bdcsn 13383 . . 3 BOUNDED {𝑥}
31, 2bdcun 13375 . 2 BOUNDED (𝑥 ∪ {𝑥})
4 df-suc 4326 . 2 suc 𝑥 = (𝑥 ∪ {𝑥})
53, 4bdceqir 13357 1 BOUNDED suc 𝑥
 Colors of variables: wff set class Syntax hints:   ∪ cun 3096  {csn 3556  suc csuc 4320  BOUNDED wbdc 13353 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1487  ax-17 1503  ax-ial 1511  ax-ext 2136  ax-bd0 13326  ax-bdor 13329  ax-bdeq 13333  ax-bdel 13334  ax-bdsb 13335 This theorem depends on definitions:  df-bi 116  df-clab 2141  df-cleq 2147  df-clel 2150  df-un 3102  df-sn 3562  df-suc 4326  df-bdc 13354 This theorem is referenced by:  bdeqsuc  13394
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