Theorem qseq12

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

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

Proof

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	$$⊢\left(A=B\wedge C=D\right)\to A/C=B/D$$