Description: An equivalence relation is symmetric. (Contributed by Peter Mazsa, 29-Dec-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | eqvrelsymrel | ⊢ ( EqvRel 𝑅 → SymRel 𝑅 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eqvrel | ⊢ ( EqvRel 𝑅 ↔ ( RefRel 𝑅 ∧ SymRel 𝑅 ∧ TrRel 𝑅 ) ) | |
2 | 1 | simp2bi | ⊢ ( EqvRel 𝑅 → SymRel 𝑅 ) |