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Theorem epel 4941
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 3175 . 2 𝑦 ∈ V
21epelc 4940 1 (𝑥 E 𝑦𝑥𝑦)
Colors of variables: wff setvar class
Syntax hints:  wb 194   class class class wbr 4577   E cep 4936
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-9 1985  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589  ax-sep 4703  ax-nul 4711  ax-pr 4827
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-eu 2461  df-mo 2462  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ne 2781  df-rab 2904  df-v 3174  df-dif 3542  df-un 3544  df-in 3546  df-ss 3553  df-nul 3874  df-if 4036  df-sn 4125  df-pr 4127  df-op 4131  df-br 4578  df-opab 4638  df-eprel 4938
This theorem is referenced by:  epse  5010  dfepfr  5012  epfrc  5013  wecmpep  5019  wetrep  5020  ordon  6851  smoiso  7323  smoiso2  7330  ordunifi  8072  ordiso2  8280  ordtypelem8  8290  wofib  8310  dford2  8377  noinfep  8417  oemapso  8439  wemapwe  8454  alephiso  8781  cflim2  8945  fin23lem27  9010  om2uzisoi  12572  bnj219  29848  efrunt  30637  dftr6  30686  dffr5  30689  elpotr  30723  dfon2lem9  30733  dfon2  30734  domep  30735  brsset  30959  dfon3  30962  brbigcup  30968  brapply  31008  brcup  31009  brcap  31010  dfint3  31022
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