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Theorem setindtrs 27087
 Description: Epsilon induction scheme without Infinity. See comments at setindtr 27086. (Contributed by Stefan O'Rear, 28-Oct-2014.)
Hypotheses
Ref Expression
setindtrs.a
setindtrs.b
setindtrs.c
Assertion
Ref Expression
setindtrs
Distinct variable groups:   ,,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   (,)   (,)   ()

Proof of Theorem setindtrs
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 setindtr 27086 . . 3
2 dfss3 3330 . . . 4
3 nfcv 2571 . . . . . . 7
4 nfsab1 2425 . . . . . . 7
53, 4nfral 2751 . . . . . 6
6 nfsab1 2425 . . . . . 6
75, 6nfim 1832 . . . . 5
8 raleq 2896 . . . . . 6
9 eleq1 2495 . . . . . 6
108, 9imbi12d 312 . . . . 5
11 setindtrs.a . . . . . 6
12 vex 2951 . . . . . . . 8
13 setindtrs.b . . . . . . . 8
1412, 13elab 3074 . . . . . . 7
1514ralbii 2721 . . . . . 6
16 abid 2423 . . . . . 6
1711, 15, 163imtr4i 258 . . . . 5
187, 10, 17chvar 1968 . . . 4
192, 18sylbi 188 . . 3
201, 19mpg 1557 . 2
21 elex 2956 . . . . 5
2221adantl 453 . . . 4
2322exlimiv 1644 . . 3
24 setindtrs.c . . . 4
2524elabg 3075 . . 3
2623, 25syl 16 . 2
2720, 26mpbid 202 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2421  wral 2697  cvv 2948   wss 3312   wtr 4294 This theorem is referenced by:  dford3lem2  27089 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-reg 7552 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-uni 4008  df-tr 4295
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