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Metamath Proof Explorer

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	$⊢ R ErALTV A \leftrightarrow S ErALTV A$

Step	Hyp	Ref	Expression
1		erALTVeq1i.1	$⊢ R = S$
2		erALTVeq1	$⊢ R = S \to (R ErALTV A \leftrightarrow S ErALTV A)$
3	1 2	ax-mp	$⊢ R ErALTV A \leftrightarrow S ErALTV A$