Theorem dmqseqeq1

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

	Ref	Expression
Assertion	dmqseqeq1	$$⊢R=S\to \left(\mathrm{dom}R/R=A\leftrightarrow \mathrm{dom}S/S=A\right)$$

Proof

Step	Hyp	Ref	Expression
1		dmqseq	$$⊢R=S\to \mathrm{dom}R/R=\mathrm{dom}S/S$$
2	1	eqeq1d	$$⊢R=S\to \left(\mathrm{dom}R/R=A\leftrightarrow \mathrm{dom}S/S=A\right)$$