Theorem errel 6563

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 6554	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1014	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1364   u. cun 3142   C_ wss 3144   `'ccnv 4640   dom cdm 4641   o. ccom 4645   Rel wrel 4646   Er wer 6551

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 982  df-er 6554

This theorem is referenced by:  ercl  6565  ersym  6566  ertr  6569  ercnv  6575  erssxp  6577  erth  6600  iinerm  6628  eqg0el  13161