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Theorem bj-bdsucel 11115
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 11114 . 2  |- BOUNDED  z  =  suc  x
21bj-bdcel 11070 1  |- BOUNDED  suc  x  e.  y
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   suc csuc 4155  BOUNDED wbd 11045
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-bd0 11046  ax-bdan 11048  ax-bdor 11049  ax-bdal 11051  ax-bdex 11052  ax-bdeq 11053  ax-bdel 11054  ax-bdsb 11055
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2614  df-un 2988  df-in 2990  df-ss 2997  df-sn 3428  df-suc 4161  df-bdc 11074
This theorem is referenced by:  bj-bdind  11167
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