Theorem epelc 4798

Description: The epsilon relationship and the membership relation are the same. (Contributed by Scott Fenton, 11-Apr-2012.)

Hypothesis

Ref	Expression
epelc.1

Assertion

Ref	Expression
epelc

Proof of Theorem epelc

Step	Hyp	Ref	Expression
1		epelc.1	. 2
2		epelg 4797	. 2
3	1, 2	ax-mp 5	1

Syntax hints:  <->wb 184  e.wcel 1818  cvv 3109   class class class wbr 4452  cep 4794

This theorem is referenced by:  epel  4799  epini  5372  smoiso  7052  smoiso2  7059  ecid  7395  ordiso2  7961  oismo  7986  cantnflt  8112  cantnfp1lem3  8120  oemapso  8122  cantnflem1b  8126  cantnflem1  8129  cantnf  8133  cantnfltOLD  8142  cantnfp1lem3OLD  8146  cantnflem1bOLD  8149  cantnflem1OLD  8152  cantnfOLD  8155  wemapwe  8160  wemapweOLD  8161  cnfcomlem  8164  cnfcom  8165  cnfcom3lem  8168  cnfcomlemOLD  8172  cnfcomOLD  8173  cnfcom3lemOLD  8176  leweon  8410  r0weon  8411  alephiso  8500  fin23lem27  8729  fpwwe2lem9  9037  ex-eprel  25154  dftr6  29179  coep  29180  coepr  29181  brsset  29539  brtxpsd  29544  brcart  29582  dfrdg4  29600  cnambfre  30063  wepwsolem  30987  dnwech  30994

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