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 )