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Theorem errel 7115
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 7106 . 2  |-  ( R  Er  A  <->  ( Rel  R  /\  dom  R  =  A  /\  ( `' R  u.  ( R  o.  R ) ) 
C_  R ) )
21simp1bi 1003 1  |-  ( R  Er  A  ->  Rel  R )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1369    u. cun 3331    C_ wss 3333   `'ccnv 4844   dom cdm 4845    o. ccom 4849   Rel wrel 4850    Er wer 7103
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 371  df-3an 967  df-er 7106
This theorem is referenced by:  ercl  7117  ersym  7118  ertr  7121  ercnv  7127  erssxp  7129  erth  7150  iiner  7177  frgpuplem  16274  topfneec  28568  prter3  29032
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