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Metamath Proof Explorer

Theorem dmqseqeq1

Description: Equality theorem for domain quotient. (Contributed by Peter Mazsa, 17-Apr-2019)

		Ref	Expression
	Assertion	dmqseqeq1	$⊢ R = S \to (dom R / R = A \leftrightarrow dom S / S = A)$

Step	Hyp	Ref	Expression
1		dmqseq	$⊢ R = S \to dom R / R = dom S / S$
2	1	eqeq1d	$⊢ R = S \to (dom R / R = A \leftrightarrow dom S / S = A)$