Theorem epel 4799

Description: The epsilon relation and the membership relation are the same. (Contributed by NM, 13-Aug-1995.)

Assertion

Ref	Expression
epel

Proof of Theorem epel

Step	Hyp	Ref	Expression
1		vex 3112	. 2
2	1	epelc 4798	1

Syntax hints:  <->wb 184   class class class wbr 4452  cep 4794

This theorem is referenced by:  epse  4867  dfepfr  4869  epfrc  4870  wecmpep  4876  wetrep  4877  ordon  6618  smoiso  7052  smoiso2  7059  ordunifi  7790  ordiso2  7961  ordtypelem8  7971  wofib  7991  dford2  8058  noinfep  8097  noinfepOLD  8098  oemapso  8122  wemapwe  8160  wemapweOLD  8161  alephiso  8500  cflim2  8664  fin23lem27  8729  om2uzisoi  12065  efrunt  29085  dftr6  29179  dffr5  29182  elpotr  29213  dfon2lem9  29223  dfon2  29224  domep  29225  brsset  29539  dfon3  29542  brbigcup  29548  brapply  29588  brcup  29589  brcap  29590  tfrqfree  29601  dfint3  29602  bnj219  33788

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-eprel 4796