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Metamath Proof Explorer

Theorem dmqseq

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

		Ref	Expression
	Assertion	dmqseq	$⊢ R = S \to dom R / R = dom S / S$

Step	Hyp	Ref	Expression
1		dmeq	$⊢ R = S \to dom R = dom S$
2		qseq12	$⊢ (dom R = dom S \land R = S) \to dom R / R = dom S / S$
3	1 2	mpancom	$⊢ R = S \to dom R / R = dom S / S$