Theorem eqvreleqi

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

	Ref	Expression
Hypothesis	eqvreleqi.1	$$⊢R=S$$
Assertion	eqvreleqi	$$⊢EqvRelR\leftrightarrow EqvRelS$$

Proof

Step	Hyp	Ref	Expression
1		eqvreleqi.1	$$⊢R=S$$
2		eqvreleq	$$⊢R=S\to \left(EqvRelR\leftrightarrow EqvRelS\right)$$
3	1 2	ax-mp	$$⊢EqvRelR\leftrightarrow EqvRelS$$