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Theorem errel 6881
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 6872 . 2  |-  ( R  Er  A  <->  ( Rel  R  /\  dom  R  =  A  /\  ( `' R  u.  ( R  o.  R ) ) 
C_  R ) )
21simp1bi 972 1  |-  ( R  Er  A  ->  Rel  R )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    u. cun 3286    C_ wss 3288   `'ccnv 4844   dom cdm 4845    o. ccom 4849   Rel wrel 4850    Er wer 6869
This theorem is referenced by:  ercl  6883  ersym  6884  ertr  6887  ercnv  6893  erssxp  6895  erth  6916  iiner  6943  frgpuplem  15367  topfneec  26269  prter3  26629
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 178  df-an 361  df-3an 938  df-er 6872
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