Theorem errel 6642

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 6633	. 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 3168   C_ wss 3170   `'ccnv 4682   dom cdm 4683   o. ccom 4687   Rel wrel 4688   Er wer 6630

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 6633

This theorem is referenced by:  ercl  6644  ersym  6645  ertr  6648  ercnv  6654  erssxp  6656  erth  6679  iinerm  6707  eqg0el  13640