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Theorem epel 4054
Description: The epsilon relation and the membership relation are the same. (Contributed by NM, 13-Aug-1995.)
Assertion
Ref Expression
epel (𝑥 E 𝑦𝑥𝑦)

Proof of Theorem epel
StepHypRef Expression
1 vex 2575 . 2 𝑦 ∈ V
21epelc 4053 1 (𝑥 E 𝑦𝑥𝑦)
Colors of variables: wff set class
Syntax hints:  wb 102   class class class wbr 3789   E cep 4049
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 638  ax-5 1350  ax-7 1351  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-8 1409  ax-10 1410  ax-11 1411  ax-i12 1412  ax-bndl 1413  ax-4 1414  ax-14 1419  ax-17 1433  ax-i9 1437  ax-ial 1441  ax-i5r 1442  ax-ext 2036  ax-sep 3900  ax-pow 3952  ax-pr 3969
This theorem depends on definitions:  df-bi 114  df-3an 896  df-tru 1260  df-nf 1364  df-sb 1660  df-eu 1917  df-mo 1918  df-clab 2041  df-cleq 2047  df-clel 2050  df-nfc 2181  df-v 2574  df-un 2947  df-in 2949  df-ss 2956  df-pw 3386  df-sn 3406  df-pr 3407  df-op 3409  df-br 3790  df-opab 3844  df-eprel 4051
This theorem is referenced by:  epse  4104  wetrep  4122  ordsoexmid  4311  zfregfr  4323  ordwe  4325  wessep  4327  reg3exmidlemwe  4328  smoiso  5945  nnwetri  6382  ordiso2  6385  frec2uzisod  9322
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