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Theorem errel 6950
Description: An equivalence relation is a relation. (Contributed by Mario Carneiro, 12-Aug-2015.)
Assertion
Ref Expression
errel  |-  ( R  Er  A  ->  Rel  R )

Proof of Theorem errel
StepHypRef Expression
1 df-er 6941 . 2  |-  ( R  Er  A  <->  ( Rel  R  /\  dom  R  =  A  /\  ( `' R  u.  ( R  o.  R ) ) 
C_  R ) )
21simp1bi 973 1  |-  ( R  Er  A  ->  Rel  R )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1654    u. cun 3307    C_ wss 3309   `'ccnv 4912   dom cdm 4913    o. ccom 4917   Rel wrel 4918    Er wer 6938
This theorem is referenced by:  ercl  6952  ersym  6953  ertr  6956  ercnv  6962  erssxp  6964  erth  6985  iiner  7012  frgpuplem  15442  topfneec  26413  prter3  26843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-er 6941
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