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Theorem bdsetindis 10094
 Description: Axiom of bounded set induction using implicit substitutions. (Contributed by BJ, 22-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdsetindis.bd BOUNDED
bdsetindis.nf0
bdsetindis.nf1
bdsetindis.nf2
bdsetindis.nf3
bdsetindis.1
bdsetindis.2
Assertion
Ref Expression
bdsetindis
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   (,,)   (,,)

Proof of Theorem bdsetindis
StepHypRef Expression
1 nfcv 2178 . . . . 5
2 bdsetindis.nf0 . . . . 5
31, 2nfralxy 2360 . . . 4
4 bdsetindis.nf1 . . . 4
53, 4nfim 1464 . . 3
6 nfcv 2178 . . . . 5
7 bdsetindis.nf3 . . . . 5
86, 7nfralxy 2360 . . . 4
9 bdsetindis.nf2 . . . 4
108, 9nfim 1464 . . 3
11 raleq 2505 . . . . 5
1211biimprd 147 . . . 4
13 bdsetindis.2 . . . . 5
1413equcoms 1594 . . . 4
1512, 14imim12d 68 . . 3
165, 10, 15cbv3 1630 . 2
17 bdsetindis.1 . . . . . 6
182, 17bj-sbime 9913 . . . . 5
1918ralimi 2384 . . . 4
2019imim1i 54 . . 3
2120alimi 1344 . 2
22 bdsetindis.bd . . 3 BOUNDED
2322ax-bdsetind 10093 . 2
2416, 21, 233syl 17 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1241  wnf 1349  wsb 1645  wral 2306  BOUNDED wbd 9932 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-bdsetind 10093 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311 This theorem is referenced by:  bj-inf2vnlem3  10097
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