Theorem dmqseqi

Description: Equality theorem for domain quotient, inference version. (Contributed by Peter Mazsa, 26-Sep-2021)

	Ref	Expression
Hypothesis	dmqseqi.1	$$⊢R=S$$
Assertion	dmqseqi	$$⊢\mathrm{dom}R/R=\mathrm{dom}S/S$$

Proof

Step	Hyp	Ref	Expression
1		dmqseqi.1	$$⊢R=S$$
2		dmqseq	$$⊢R=S\to \mathrm{dom}R/R=\mathrm{dom}S/S$$
3	1 2	ax-mp	$$⊢\mathrm{dom}R/R=\mathrm{dom}S/S$$