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Theorem rele 4954
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 4736 . 2  |-  _E  =  { <. x ,  y
>.  |  x  e.  y }
21relopabi 4950 1  |-  Rel  _E
Colors of variables: wff setvar class
Syntax hints:    _E cep 4734   Rel wrel 4830
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-9 1848  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382  ax-sep 4519  ax-nul 4527  ax-pr 4632
This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-3an 978  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-ne 2602  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3063  df-dif 3419  df-un 3421  df-in 3423  df-ss 3430  df-nul 3741  df-if 3888  df-sn 3975  df-pr 3977  df-op 3981  df-opab 4456  df-eprel 4736  df-xp 4831  df-rel 4832
This theorem is referenced by:  cnambfre  31448
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