Theorem erALTVeq1d

Description: Equality theorem for equivalence relation on domain quotient, deduction version. (Contributed by Peter Mazsa, 25-Sep-2021)

	Ref	Expression
Hypothesis	erALTVeq1d.1	⊢ ( 𝜑 → 𝑅 = 𝑆 )
Assertion	erALTVeq1d	⊢ ( 𝜑 → ( 𝑅 ErALTV 𝐴 ↔ 𝑆 ErALTV 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		erALTVeq1d.1	⊢ ( 𝜑 → 𝑅 = 𝑆 )
2		erALTVeq1	⊢ ( 𝑅 = 𝑆 → ( 𝑅 ErALTV 𝐴 ↔ 𝑆 ErALTV 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝑅 ErALTV 𝐴 ↔ 𝑆 ErALTV 𝐴 ) )