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Theorem bdcsuc 11417
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 11385 . . 3 BOUNDED 𝑥
2 bdcsn 11407 . . 3 BOUNDED {𝑥}
31, 2bdcun 11399 . 2 BOUNDED (𝑥 ∪ {𝑥})
4 df-suc 4189 . 2 suc 𝑥 = (𝑥 ∪ {𝑥})
53, 4bdceqir 11381 1 BOUNDED suc 𝑥
Colors of variables: wff set class
Syntax hints:  cun 2995  {csn 3441  suc csuc 4183  BOUNDED wbdc 11377
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 11350  ax-bdor 11353  ax-bdeq 11357  ax-bdel 11358  ax-bdsb 11359
This theorem depends on definitions:  df-bi 115  df-clab 2075  df-cleq 2081  df-clel 2084  df-un 3001  df-sn 3447  df-suc 4189  df-bdc 11378
This theorem is referenced by:  bdeqsuc  11418
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