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Theorem bj-bdsucel 10002
 Description: Boundedness of the formula "the successor of the setvar 𝑥 belongs to the setvar 𝑦". (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
bj-bdsucel BOUNDED suc 𝑥𝑦

Proof of Theorem bj-bdsucel
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 bdeqsuc 10001 . 2 BOUNDED 𝑧 = suc 𝑥
21bj-bdcel 9957 1 BOUNDED suc 𝑥𝑦
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  suc csuc 4102  BOUNDED wbd 9932 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-bd0 9933  ax-bdan 9935  ax-bdor 9936  ax-bdal 9938  ax-bdex 9939  ax-bdeq 9940  ax-bdel 9941  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-sn 3381  df-suc 4108  df-bdc 9961 This theorem is referenced by:  bj-bdind  10054
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