Theorem errel 6820

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 6811	. 2 |- ( R Er A <-> ( Rel R /\ dom R = A /\ ( `' R u. ( R o. R ) ) C_ R ) )
2	1	simp1bi 1043	1 |- ( R Er A -> Rel R )

This proof depends on syntax axioms:   -> wi 4   = wceq 1402   u. cun 3218   C_ wss 3220   `'ccnv 4775   dom cdm 4776   o. ccom 4780   Rel wrel 4781   Er wer 6808

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117  df-3an 1011  df-er 6811

This theorem is used by:  ercl  6822  ersym  6823  ertr  6826  ercnv  6832  erssxp  6834  erth  6857  iinerm  6885  eqg0el  14091