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Metamath Proof Explorer

Theorem eqvreleqd

Description: Equality theorem for equivalence relation, deduction version. (Contributed by Peter Mazsa, 23-Sep-2021)

		Ref	Expression
	Hypothesis	eqvreleqd.1	$⊢ φ \to R = S$
	Assertion	eqvreleqd	$⊢ φ \to (EqvRel R \leftrightarrow EqvRel S)$

Step	Hyp	Ref	Expression
1		eqvreleqd.1	$⊢ φ \to R = S$
2		eqvreleq	$⊢ R = S \to (EqvRel R \leftrightarrow EqvRel S)$
3	1 2	syl	$⊢ φ \to (EqvRel R \leftrightarrow EqvRel S)$