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Theorem errel 6051
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
StepHypRef Expression
1 df-er 6042 . 2 (𝑅 Er A ↔ (Rel 𝑅 dom 𝑅 = A (𝑅 ∪ (𝑅𝑅)) ⊆ 𝑅))
21simp1bi 918 1 (𝑅 Er A → Rel 𝑅)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242  cun 2909  wss 2911  ccnv 4287  dom cdm 4288  ccom 4292  Rel wrel 4293   Er wer 6039
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110  df-3an 886  df-er 6042
This theorem is referenced by:  ercl  6053  ersym  6054  ertr  6057  ercnv  6063  erssxp  6065  erth  6086  iinerm  6114
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