Theorem dmqseqeq1i

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

	Ref	Expression
Hypothesis	dmqseqeq1i.1	$$⊢R=S$$
Assertion	dmqseqeq1i	$$⊢\mathrm{dom}R/R=A\leftrightarrow \mathrm{dom}S/S=A$$

Proof

Step	Hyp	Ref	Expression
1		dmqseqeq1i.1	$$⊢R=S$$
2		dmqseqeq1	$$⊢R=S\to \left(\mathrm{dom}R/R=A\leftrightarrow \mathrm{dom}S/S=A\right)$$
3	1 2	ax-mp	$$⊢\mathrm{dom}R/R=A\leftrightarrow \mathrm{dom}S/S=A$$