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Theorem errel 7356
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 7347 . 2  |-  ( R  Er  A  <->  ( Rel  R  /\  dom  R  =  A  /\  ( `' R  u.  ( R  o.  R ) ) 
C_  R ) )
21simp1bi 1012 1  |-  ( R  Er  A  ->  Rel  R )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1405    u. cun 3411    C_ wss 3413   `'ccnv 4821   dom cdm 4822    o. ccom 4826   Rel wrel 4827    Er wer 7344
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 185  df-an 369  df-3an 976  df-er 7347
This theorem is referenced by:  ercl  7358  ersym  7359  ertr  7362  ercnv  7368  erssxp  7370  erth  7392  iiner  7419  frgpuplem  17112  ismntop  28442  topfneec  30570  prter3  31885
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