Theorem errel 6710

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 6701	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1038	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1397   u. cun 3198   C_ wss 3200   `'ccnv 4724   dom cdm 4725   o. ccom 4729   Rel wrel 4730   Er wer 6698

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 1006  df-er 6701

This theorem is referenced by:  ercl  6712  ersym  6713  ertr  6716  ercnv  6722  erssxp  6724  erth  6747  iinerm  6775  eqg0el  13815