Theorem errel 6446

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 6437	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 997	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1332   u. cun 3074   C_ wss 3076   `'ccnv 4546   dom cdm 4547   o. ccom 4551   Rel wrel 4552   Er wer 6434

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105

This theorem depends on definitions:  df-bi 116  df-3an 965  df-er 6437

This theorem is referenced by:  ercl  6448  ersym  6449  ertr  6452  ercnv  6458  erssxp  6460  erth  6481  iinerm  6509