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Theorem errel 7317
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 7308 . 2  |-  ( R  Er  A  <->  ( Rel  R  /\  dom  R  =  A  /\  ( `' R  u.  ( R  o.  R ) ) 
C_  R ) )
21simp1bi 1011 1  |-  ( R  Er  A  ->  Rel  R )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1379    u. cun 3474    C_ wss 3476   `'ccnv 4998   dom cdm 4999    o. ccom 5003   Rel wrel 5004    Er wer 7305
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 975  df-er 7308
This theorem is referenced by:  ercl  7319  ersym  7320  ertr  7323  ercnv  7329  erssxp  7331  erth  7353  iiner  7380  frgpuplem  16586  ismntop  27644  topfneec  29763  prter3  30227
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