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Theorem elec 6699
 Description: Membership in an equivalence class. Theorem 72 of [Suppes] p. 82. (Contributed by NM, 23-Jul-1995.)
Hypotheses
Ref Expression
elec.1
elec.2
Assertion
Ref Expression
elec

Proof of Theorem elec
StepHypRef Expression
1 elec.1 . 2
2 elec.2 . 2
3 elecg 6698 . 2
41, 2, 3mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wb 176   wcel 1684  cvv 2788   class class class wbr 4023  cec 6658 This theorem is referenced by:  ecid  6724  sylow2alem2  14929  sylow2a  14930  sylow2blem1  14931  efgval2  15033  efgrelexlemb  15059  efgcpbllemb  15064  frgpnabllem1  15161  tgpconcomp  17795  divstgphaus  17805  vitalilem2  18964  vitalilem3  18965  isbndx  26506  prtlem10  26733  prtlem19  26746  prter3  26750 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-xp 4695  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-ec 6662
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