Theorem qseq12d

Description: Equality theorem for quotient set, deduction form. (Contributed by Steven Nguyen, 30-Apr-2023)

	Ref	Expression
Hypotheses	qseq12d.1	$$⊢\phi \to A=B$$
	qseq12d.2	$$⊢\phi \to C=D$$
Assertion	qseq12d	$$⊢\phi \to A/C=B/D$$

Proof

Step	Hyp	Ref	Expression
1		qseq12d.1	$$⊢\phi \to A=B$$
2		qseq12d.2	$$⊢\phi \to C=D$$
3		qseq12	$$⊢\left(A=B\wedge C=D\right)\to A/C=B/D$$
4	1 2 3	syl2anc	$$⊢\phi \to A/C=B/D$$