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Metamath Proof Explorer

Theorem qseq12

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

		Ref	Expression
	Assertion	qseq12	$⊢ (A = B \land C = D) \to A / C = B / D$

Step	Hyp	Ref	Expression
1		qseq1	$⊢ A = B \to A / C = B / C$
2		qseq2	$⊢ C = D \to B / C = B / D$
3	1 2	sylan9eq	$⊢ (A = B \land C = D) \to A / C = B / D$