Theorem errel 6115

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 6106	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 919	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1243   u. cun 2915   C_ wss 2917   `'ccnv 4344   dom cdm 4345   o. ccom 4349   Rel wrel 4350   Er wer 6103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99

This theorem depends on definitions:  df-bi 110  df-3an 887  df-er 6106

This theorem is referenced by:  ercl  6117  ersym  6118  ertr  6121  ercnv  6127  erssxp  6129  erth  6150  iinerm  6178