Metamath Proof Explorer


Theorem eqvrelrefrel

Description: An equivalence relation is reflexive. (Contributed by Peter Mazsa, 29-Dec-2021)

Ref Expression
Assertion eqvrelrefrel ⊢ EqvRel R → RefRel R

Proof

Step Hyp Ref Expression
1 df-eqvrel ⊢ EqvRel R ↔ RefRel R ∧ SymRel R ∧ TrRel R
2 1 simp1bi ⊢ EqvRel R → RefRel R