Theorem errel 6438

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 6429	. 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 3069   C_ wss 3071   `'ccnv 4538   dom cdm 4539   o. ccom 4543   Rel wrel 4544   Er wer 6426

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 6429

This theorem is referenced by:  ercl  6440  ersym  6441  ertr  6444  ercnv  6450  erssxp  6452  erth  6473  iinerm  6501