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Theorem bj-bdsucel 13877
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 13876 . 2 BOUNDED 𝑧 = suc 𝑥
21bj-bdcel 13832 1 BOUNDED suc 𝑥𝑦
Colors of variables: wff set class
Syntax hints:  wcel 2141  suc csuc 4348  BOUNDED wbd 13807
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-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-bd0 13808  ax-bdan 13810  ax-bdor 13811  ax-bdal 13813  ax-bdex 13814  ax-bdeq 13815  ax-bdel 13816  ax-bdsb 13817
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-rex 2454  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-sn 3587  df-suc 4354  df-bdc 13836
This theorem is referenced by:  bj-bdind  13925
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