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Theorem errel 7372
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 7363 . 2  |-  ( R  Er  A  <->  ( Rel  R  /\  dom  R  =  A  /\  ( `' R  u.  ( R  o.  R ) ) 
C_  R ) )
21simp1bi 1020 1  |-  ( R  Er  A  ->  Rel  R )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1437    u. cun 3431    C_ wss 3433   `'ccnv 4845   dom cdm 4846    o. ccom 4850   Rel wrel 4851    Er wer 7360
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 188  df-an 372  df-3an 984  df-er 7363
This theorem is referenced by:  ercl  7374  ersym  7375  ertr  7378  ercnv  7384  erssxp  7386  erth  7408  iiner  7435  frgpuplem  17400  ismntop  28819  topfneec  30997  prter3  32366
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