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Theorem epel 4324
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 2804 . 2  |-  y  e. 
_V
21epelc 4323 1  |-  ( x  _E  y  <->  x  e.  y )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   class class class wbr 4039    _E cep 4319
This theorem is referenced by:  epse  4392  dfepfr  4394  epfrc  4395  wecmpep  4401  wetrep  4402  ordon  4590  smoiso  6395  smoiso2  6402  ordunifi  7123  ordiso2  7246  ordtypelem8  7256  wofib  7276  dford2  7337  noinfep  7376  noinfepOLD  7377  oemapso  7400  wemapwe  7416  alephiso  7741  cflim2  7905  fin23lem27  7970  om2uzisoi  11033  efrunt  24074  dftr6  24178  dffr5  24181  elpotr  24208  dfon2lem9  24218  dfon2  24219  domep  24220  brsset  24500  dfon3  24503  brbigcup  24509  brapply  24548  tfrqfree  24561  bnj219  29077
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-eprel 4321
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