Theorem errel 6629

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 6620	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1015	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1373   u. cun 3164   C_ wss 3166   `'ccnv 4674   dom cdm 4675   o. ccom 4679   Rel wrel 4680   Er wer 6617

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 983  df-er 6620

This theorem is referenced by:  ercl  6631  ersym  6632  ertr  6635  ercnv  6641  erssxp  6643  erth  6666  iinerm  6694  eqg0el  13565