Theorem dmqseq

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

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

Proof

Step	Hyp	Ref	Expression
1		dmeq	$$⊢R=S\to \mathrm{dom}R=\mathrm{dom}S$$
2		qseq12	$$⊢\left(\mathrm{dom}R=\mathrm{dom}S\wedge R=S\right)\to \mathrm{dom}R/R=\mathrm{dom}S/S$$
3	1 2	mpancom	$$⊢R=S\to \mathrm{dom}R/R=\mathrm{dom}S/S$$