Theorem errel 6138

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 6129	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 953	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1284   u. cun 2971   C_ wss 2973   `'ccnv 4362   dom cdm 4363   o. ccom 4367   Rel wrel 4368   Er wer 6126

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-3an 921  df-er 6129

This theorem is referenced by:  ercl  6140  ersym  6141  ertr  6144  ercnv  6150  erssxp  6152  erth  6173  iinerm  6201