Theorem errel 6546

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 6537	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1012	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1353   u. cun 3129   C_ wss 3131   `'ccnv 4627   dom cdm 4628   o. ccom 4632   Rel wrel 4633   Er wer 6534

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This theorem depends on definitions:  df-bi 117  df-3an 980  df-er 6537

This theorem is referenced by:  ercl  6548  ersym  6549  ertr  6552  ercnv  6558  erssxp  6560  erth  6581  iinerm  6609