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Theorem bj-bdsucel 9317
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 y

Proof of Theorem bj-bdsucel
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 bdeqsuc 9316 . 2 BOUNDED z = suc x
21bj-bdcel 9272 1 BOUNDED suc x y
Colors of variables: wff set class
Syntax hints:   wcel 1390  suc csuc 4068  BOUNDED wbd 9247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-bd0 9248  ax-bdan 9250  ax-bdor 9251  ax-bdal 9253  ax-bdex 9254  ax-bdeq 9255  ax-bdel 9256  ax-bdsb 9257
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-suc 4074  df-bdc 9276
This theorem is referenced by:  bj-bdind  9365
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