Theorem errel 7751

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

Step	Hyp	Ref	Expression
1		df-er 7742	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1076	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1483   u. cun 3572   C_ wss 3574   `'ccnv 5113   dom cdm 5114   o. ccom 5118   Rel wrel 5119   Er wer 7739

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 197  df-an 386  df-3an 1039  df-er 7742

This theorem is referenced by:  ercl  7753  ersym  7754  ertr  7757  ercnv  7763  erssxp  7765  erth  7791  iiner  7819  frgpuplem  18185  ismntop  30070  topfneec  32350  prter3  34167