Theorem epel 2834

Description: The epsilon relation and the membership relation are the same.

Assertion

Ref	Expression
epel	|- (xEy <-> x e. y)

Proof of Theorem epel

Step	Hyp	Ref	Expression
1		visset 1813	. 2 |- x e. V
2		visset 1813	. 2 |- y e. V
3	1, 2	epelc 2833	1 |- (xEy <-> x e. y)

Syntax hints:   <-> wb 146   e. wcel 958   class class class wbr 2619  Ecep 2830

This theorem is referenced by:  efrirr 2928  efrn2lp 2929  epne3 2930  dfepfr 2932  epfrc 2933  wecmpep 2941  wetrep 2942  ordon 2987  noinfep 4640  alephiso 4892  ltpiord 5015

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-13 969  ax-14 970  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-sep 2703  ax-pow 2742  ax-pr 2779

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1587  df-v 1812  df-dif 2049  df-un 2050  df-in 2051  df-ss 2053  df-nul 2281  df-pw 2402  df-sn 2412  df-pr 2413  df-op 2416  df-br 2620  df-opab 2667  df-eprel 2832

Copyright terms: Public domain