Metamath Proof Explorer

Theorem eqvrelsymrel

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

Ref Expression
Assertion eqvrelsymrel 
|- ( EqvRel R -> SymRel R )

Proof

Step Hyp Ref Expression
1 df-eqvrel 
 |-  ( EqvRel R <-> ( RefRel R /\ SymRel R /\ TrRel R ) )
2 1 simp2bi 
 |-  ( EqvRel R -> SymRel R )