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Theorem rele 5697
 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 5463 . 2 E = {⟨𝑥, 𝑦⟩ ∣ 𝑥𝑦}
21relopabi 5692 1 Rel E
 Colors of variables: wff setvar class Syntax hints:   E cep 5462  Rel wrel 5558 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2797 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2804  df-cleq 2818  df-clel 2897  df-nfc 2967  df-rab 3151  df-v 3501  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4470  df-sn 4564  df-pr 4566  df-op 4570  df-opab 5125  df-eprel 5463  df-xp 5559  df-rel 5560 This theorem is referenced by:  bj-epelg  34243  bj-epelb  34244  cnambfre  34809  brcnvep  35396
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