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Theorem bj-bdsucel 12914
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 12913 . 2 BOUNDED 𝑧 = suc 𝑥
21bj-bdcel 12869 1 BOUNDED suc 𝑥𝑦
Colors of variables: wff set class
Syntax hints:  wcel 1463  suc csuc 4255  BOUNDED wbd 12844
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-bd0 12845  ax-bdan 12847  ax-bdor 12848  ax-bdal 12850  ax-bdex 12851  ax-bdeq 12852  ax-bdel 12853  ax-bdsb 12854
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rex 2397  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-sn 3501  df-suc 4261  df-bdc 12873
This theorem is referenced by:  bj-bdind  12962
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