Theorem eqvreleqd

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

	Ref	Expression
Hypothesis	eqvreleqd.1	⊢ ( 𝜑 → 𝑅 = 𝑆 )
Assertion	eqvreleqd	⊢ ( 𝜑 → ( EqvRel 𝑅 ↔ EqvRel 𝑆 ) )

Proof

Step	Hyp	Ref	Expression
1		eqvreleqd.1	⊢ ( 𝜑 → 𝑅 = 𝑆 )
2		eqvreleq	⊢ ( 𝑅 = 𝑆 → ( EqvRel 𝑅 ↔ EqvRel 𝑆 ) )
3	1 2	syl	⊢ ( 𝜑 → ( EqvRel 𝑅 ↔ EqvRel 𝑆 ) )