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Theorem rele 5827
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 5580 . 2 E = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
21relopabiv 5820 1 Rel E
Colors of variables: wff setvar class
Syntax hints:   E cep 5579  Rel wrel 5681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-v 3476  df-in 3955  df-ss 3965  df-opab 5211  df-eprel 5580  df-xp 5682  df-rel 5683
This theorem is referenced by:  bj-epelg  35944  bj-epelb  35945  cnambfre  36531  brcnvep  37128
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