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Theorem rele 4851
Description: The membership relation is a relation. (Contributed by NM, 26-Apr-1998.) (Revised by Mario Carneiro, 21-Dec-2013.)
Assertion
Ref Expression
rele  |-  Rel  _E

Proof of Theorem rele
Dummy variables  x  y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-eprel 4342 . 2  |-  _E  =  { <. x ,  y
>.  |  x  e.  y }
21relopabi 4848 1  |-  Rel  _E
Colors of variables: wff set class
Syntax hints:    e. wcel 1701    _E cep 4340   Rel wrel 4731
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-14 1705  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178  ax-nul 4186  ax-pr 4251
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ne 2481  df-ral 2582  df-rex 2583  df-rab 2586  df-v 2824  df-dif 3189  df-un 3191  df-in 3193  df-ss 3200  df-nul 3490  df-if 3600  df-sn 3680  df-pr 3681  df-op 3683  df-opab 4115  df-eprel 4342  df-xp 4732  df-rel 4733
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