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Theorem epel 5061
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 3234 . 2 𝑦 ∈ V
21epelc 5060 1 (𝑥 E 𝑦𝑥𝑦)
Colors of variables: wff setvar class
Syntax hints:  wb 196   class class class wbr 4685   E cep 5057
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pr 4936
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ne 2824  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-opab 4746  df-eprel 5058
This theorem is referenced by:  epse  5126  dfepfr  5128  epfrc  5129  wecmpep  5135  wetrep  5136  ordon  7024  smoiso  7504  smoiso2  7511  ordunifi  8251  ordiso2  8461  ordtypelem8  8471  wofib  8491  dford2  8555  noinfep  8595  oemapso  8617  wemapwe  8632  alephiso  8959  cflim2  9123  fin23lem27  9188  om2uzisoi  12793  bnj219  30927  efrunt  31716  dftr6  31766  dffr5  31769  elpotr  31810  dfon2lem9  31820  dfon2  31821  domep  31822  brsset  32121  dfon3  32124  brbigcup  32130  brapply  32170  brcup  32171  brcap  32172  dfint3  32184  dfssr2  34389
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