Theorem erALTVeq1i

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

	Ref	Expression
Hypothesis	erALTVeq1i.1	$$⊢R=S$$
Assertion	erALTVeq1i	$$⊢RErALTVA\leftrightarrow SErALTVA$$

Proof

Step	Hyp	Ref	Expression
1		erALTVeq1i.1	$$⊢R=S$$
2		erALTVeq1	$$⊢R=S\to \left(RErALTVA\leftrightarrow SErALTVA\right)$$
3	1 2	ax-mp	$$⊢RErALTVA\leftrightarrow SErALTVA$$