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Theorem epel 4029
 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 2560 . 2 𝑦 ∈ V
21epelc 4028 1 (𝑥 E 𝑦𝑥𝑦)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   class class class wbr 3764   E cep 4024 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-eprel 4026 This theorem is referenced by:  epse  4079  wetrep  4097  ordsoexmid  4286  zfregfr  4298  ordwe  4300  wessep  4302  reg3exmidlemwe  4303  smoiso  5917  nnwetri  6354  ordiso2  6357  frec2uzisod  9193
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