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Theorem tfis2f 4250
Description: Transfinite Induction Schema, using implicit substitution. (Contributed by NM, 18-Aug-1994.)
Hypotheses
Ref Expression
tfis2f.1  F/
tfis2f.2
tfis2f.3  On
Assertion
Ref Expression
tfis2f  On
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem tfis2f
StepHypRef Expression
1 tfis2f.1 . . . . 5  F/
2 tfis2f.2 . . . . 5
31, 2sbie 1671 . . . 4
43ralbii 2324 . . 3
5 tfis2f.3 . . 3  On
64, 5syl5bi 141 . 2  On
76tfis 4249 1  On
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   F/wnf 1346   wcel 1390  wsb 1642  wral 2300   Oncon0 4066
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-setind 4220
This theorem depends on definitions:  df-bi 110  df-3an 886  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-rab 2309  df-v 2553  df-in 2918  df-ss 2925  df-uni 3572  df-tr 3846  df-iord 4069  df-on 4071
This theorem is referenced by:  tfis2  4251  tfri3  5894
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