Theorem errel 6299

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 6290	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 958	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1289   u. cun 2997   C_ wss 2999   `'ccnv 4437   dom cdm 4438   o. ccom 4442   Rel wrel 4443   Er wer 6287

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-3an 926  df-er 6290

This theorem is referenced by:  ercl  6301  ersym  6302  ertr  6305  ercnv  6311  erssxp  6313  erth  6334  iinerm  6362