Theorem errel 6689

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 6680	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1036	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1395   u. cun 3195   C_ wss 3197   `'ccnv 4718   dom cdm 4719   o. ccom 4723   Rel wrel 4724   Er wer 6677

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 1004  df-er 6680

This theorem is referenced by:  ercl  6691  ersym  6692  ertr  6695  ercnv  6701  erssxp  6703  erth  6726  iinerm  6754  eqg0el  13766