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Theorem epel 4110
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 2622 . 2 𝑦 ∈ V
21epelc 4109 1 (𝑥 E 𝑦𝑥𝑦)
Colors of variables: wff set class
Syntax hints:  wb 103   class class class wbr 3837   E cep 4105
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-pow 4001  ax-pr 4027
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3001  df-in 3003  df-ss 3010  df-pw 3427  df-sn 3447  df-pr 3448  df-op 3450  df-br 3838  df-opab 3892  df-eprel 4107
This theorem is referenced by:  epse  4160  wetrep  4178  ordsoexmid  4368  zfregfr  4379  ordwe  4381  wessep  4383  reg3exmidlemwe  4384  smoiso  6049  nnwetri  6606  ordiso2  6707  frec2uzisod  9779  nnti  11538
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