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Metamath Proof Explorer

Theorem eqvrelsymrel

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

		Ref	Expression
	Assertion	eqvrelsymrel	$⊢ EqvRel R \to SymRel R$

Step	Hyp	Ref	Expression
1		df-eqvrel	$⊢ EqvRel R \leftrightarrow (RefRel R \land SymRel R \land TrRel R)$
2	1	simp2bi	$⊢ EqvRel R \to SymRel R$