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Theorem bj-bdsucel 11203
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 11202 . 2 BOUNDED 𝑧 = suc 𝑥
21bj-bdcel 11158 1 BOUNDED suc 𝑥𝑦
Colors of variables: wff set class
Syntax hints:  wcel 1436  suc csuc 4165  BOUNDED wbd 11133
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-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-bd0 11134  ax-bdan 11136  ax-bdor 11137  ax-bdal 11139  ax-bdex 11140  ax-bdeq 11141  ax-bdel 11142  ax-bdsb 11143
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-sn 3437  df-suc 4171  df-bdc 11162
This theorem is referenced by:  bj-bdind  11255
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