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Theorem epel 4310
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 2755 . 2  |-  y  e. 
_V
21epelc 4309 1  |-  ( x  _E  y  <->  x  e.  y )
Colors of variables: wff set class
Syntax hints:    <-> wb 105   class class class wbr 4018    _E cep 4305
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4192  ax-pr 4227
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-br 4019  df-opab 4080  df-eprel 4307
This theorem is referenced by:  epse  4360  wetrep  4378  ordsoexmid  4579  zfregfr  4591  ordwe  4593  wessep  4595  reg3exmidlemwe  4596  smoiso  6327  nnwetri  6944  ordiso2  7064  frec2uzisod  10438  nnti  15203
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