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	|- ( ph -> R = S )
Assertion	erALTVeq1d	|- ( ph -> ( R ErALTV A <-> S ErALTV A ) )

Proof

Step	Hyp	Ref	Expression
1		erALTVeq1d.1	|- ( ph -> R = S )
2		erALTVeq1	|- ( R = S -> ( R ErALTV A <-> S ErALTV A ) )
3	1 2	syl	|- ( ph -> ( R ErALTV A <-> S ErALTV A ) )