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Theorem tfis2 4836
 Description: Transfinite Induction Schema, using implicit substitution. (Contributed by NM, 18-Aug-1994.)
Hypotheses
Ref Expression
tfis2.1
tfis2.2
Assertion
Ref Expression
tfis2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem tfis2
StepHypRef Expression
1 nfv 1629 . 2
2 tfis2.1 . 2
3 tfis2.2 . 2
41, 2, 3tfis2f 4835 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wcel 1725  wral 2705  con0 4581 This theorem is referenced by:  tfis3  4837  smogt  6629  tfrlem1  6636  findcard3  7350  ordiso2  7484  cantnf  7649  cfsmolem  8150  fpwwe2lem8  8512  nqereu  8806 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403  ax-un 4701 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-tr 4303  df-eprel 4494  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-on 4585
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