Theorem errel 6506

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 6497	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1002	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1343   u. cun 3113   C_ wss 3115   `'ccnv 4602   dom cdm 4603   o. ccom 4607   Rel wrel 4608   Er wer 6494

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-3an 970  df-er 6497

This theorem is referenced by:  ercl  6508  ersym  6509  ertr  6512  ercnv  6518  erssxp  6520  erth  6541  iinerm  6569