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Theorem eqvrelrefrel 36711
Description: An equivalence relation is reflexive. (Contributed by Peter Mazsa, 29-Dec-2021.)
Assertion
Ref Expression
eqvrelrefrel ( EqvRel 𝑅 → RefRel 𝑅)

Proof of Theorem eqvrelrefrel
StepHypRef Expression
1 df-eqvrel 36698 . 2 ( EqvRel 𝑅 ↔ ( RefRel 𝑅 ∧ SymRel 𝑅 ∧ TrRel 𝑅))
21simp1bi 1144 1 ( EqvRel 𝑅 → RefRel 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wi 4   RefRel wrefrel 36339   SymRel wsymrel 36345   TrRel wtrrel 36348   EqvRel weqvrel 36350
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1088  df-eqvrel 36698
This theorem is referenced by: (None)
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