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Theorem bj-bdind 9389
Description: Boundedness of the formula "the setvar x is an inductive class". (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
bj-bdind BOUNDED Ind x

Proof of Theorem bj-bdind
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 bj-bd0el 9323 . . 3 BOUNDED x
2 bj-bdsucel 9337 . . . 4 BOUNDED suc y x
32ax-bdal 9273 . . 3 BOUNDED y x suc y x
41, 3ax-bdan 9270 . 2 BOUNDED (∅ x y x suc y x)
5 df-bj-ind 9386 . 2 (Ind x ↔ (∅ x y x suc y x))
64, 5bd0r 9280 1 BOUNDED Ind x
Colors of variables: wff set class
Syntax hints:   wa 97   wcel 1390  wral 2300  c0 3218  suc csuc 4068  BOUNDED wbd 9267  Ind wind 9385
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-in1 544  ax-in2 545  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-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-bd0 9268  ax-bdim 9269  ax-bdan 9270  ax-bdor 9271  ax-bdn 9272  ax-bdal 9273  ax-bdex 9274  ax-bdeq 9275  ax-bdel 9276  ax-bdsb 9277
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  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-dif 2914  df-un 2916  df-in 2918  df-ss 2925  df-nul 3219  df-sn 3373  df-suc 4074  df-bdc 9296  df-bj-ind 9386
This theorem is referenced by: (None)
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