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	$$⊢\phi \to R=S$$
Assertion	erALTVeq1d	$$⊢\phi \to \left(RErALTVA\leftrightarrow SErALTVA\right)$$

Proof

Step	Hyp	Ref	Expression
1		erALTVeq1d.1	$$⊢\phi \to R=S$$
2		erALTVeq1	$$⊢R=S\to \left(RErALTVA\leftrightarrow SErALTVA\right)$$
3	1 2	syl	$$⊢\phi \to \left(RErALTVA\leftrightarrow SErALTVA\right)$$