Theorem errel 6431

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 6422	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 996	1 |- ( R Er A -> Rel R )

Syntax hints:   -> wi 4   = wceq 1331   u. cun 3064   C_ wss 3066   `'ccnv 4533   dom cdm 4534   o. ccom 4538   Rel wrel 4539   Er wer 6419

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 964  df-er 6422

This theorem is referenced by:  ercl  6433  ersym  6434  ertr  6437  ercnv  6443  erssxp  6445  erth  6466  iinerm  6494