Theorem eqvreleqd

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

	Ref	Expression
Hypothesis	eqvreleqd.1	$$⊢\phi \to R=S$$
Assertion	eqvreleqd	$$⊢\phi \to \left(EqvRelR\leftrightarrow EqvRelS\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqvreleqd.1	$$⊢\phi \to R=S$$
2		eqvreleq	$$⊢R=S\to \left(EqvRelR\leftrightarrow EqvRelS\right)$$
3	1 2	syl	$$⊢\phi \to \left(EqvRelR\leftrightarrow EqvRelS\right)$$