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Theorem bj-bdsucel 13007
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  x  e.  y

Proof of Theorem bj-bdsucel
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 bdeqsuc 13006 . 2  |- BOUNDED  z  =  suc  x
21bj-bdcel 12962 1  |- BOUNDED  suc  x  e.  y
Colors of variables: wff set class
Syntax hints:    e. wcel 1465   suc csuc 4257  BOUNDED wbd 12937
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-bd0 12938  ax-bdan 12940  ax-bdor 12941  ax-bdal 12943  ax-bdex 12944  ax-bdeq 12945  ax-bdel 12946  ax-bdsb 12947
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-suc 4263  df-bdc 12966
This theorem is referenced by:  bj-bdind  13055
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