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Theorem bj-bdsucel 11773
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 11772 . 2  |- BOUNDED  z  =  suc  x
21bj-bdcel 11728 1  |- BOUNDED  suc  x  e.  y
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   suc csuc 4192  BOUNDED wbd 11703
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-bd0 11704  ax-bdan 11706  ax-bdor 11707  ax-bdal 11709  ax-bdex 11710  ax-bdeq 11711  ax-bdel 11712  ax-bdsb 11713
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-sn 3452  df-suc 4198  df-bdc 11732
This theorem is referenced by:  bj-bdind  11825
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