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Theorem epel 4308
Description: The epsilon relation and the membership relation are the same. (Contributed by NM, 13-Aug-1995.)
Assertion
Ref Expression
epel  |-  ( x  _E  y  <->  x  e.  y )

Proof of Theorem epel
StepHypRef Expression
1 vex 2791 . 2  |-  y  e. 
_V
21epelc 4307 1  |-  ( x  _E  y  <->  x  e.  y )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   class class class wbr 4023    _E cep 4303
This theorem is referenced by:  epse  4376  dfepfr  4378  epfrc  4379  wecmpep  4385  wetrep  4386  ordon  4574  smoiso  6379  smoiso2  6386  ordunifi  7107  ordiso2  7230  ordtypelem8  7240  wofib  7260  dford2  7321  noinfep  7360  noinfepOLD  7361  oemapso  7384  wemapwe  7400  alephiso  7725  cflim2  7889  fin23lem27  7954  om2uzisoi  11017  efrunt  24059  dftr6  24107  dffr5  24110  elpotr  24137  dfon2lem9  24147  dfon2  24148  domep  24149  brsset  24429  dfon3  24432  brbigcup  24438  brapply  24477  tfrqfree  24489  bnj219  28761
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-rab 2552  df-v 2790  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-eprel 4305
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