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Theorem errel 6669
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 6660 . 2  |-  ( R  Er  A  <->  ( Rel  R  /\  dom  R  =  A  /\  ( `' R  u.  ( R  o.  R ) ) 
C_  R ) )
21simp1bi 970 1  |-  ( R  Er  A  ->  Rel  R )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    u. cun 3150    C_ wss 3152   `'ccnv 4688   dom cdm 4689    o. ccom 4693   Rel wrel 4694    Er wer 6657
This theorem is referenced by:  ercl  6671  ersym  6672  ertr  6675  ercnv  6681  erssxp  6683  erth  6704  iiner  6731  frgpuplem  15081  topfneec  26291  prter3  26750
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-er 6660
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