Theorem dmqscoelseq

Description: Two ways to express the equality of the domain quotient of the coelements on the class A with the class A . (Contributed by Peter Mazsa, 26-Sep-2021)

	Ref	Expression
Assertion	dmqscoelseq	$$⊢\mathrm{dom}\sim A/\sim A=A\leftrightarrow \bigcup A/\sim A=A$$

Proof

Step	Hyp	Ref	Expression
1		dmcoels	$$⊢\mathrm{dom}\sim A=\bigcup A$$
2	1	qseq1i	$$⊢\mathrm{dom}\sim A/\sim A=\bigcup A/\sim A$$
3	2	eqeq1i	$$⊢\mathrm{dom}\sim A/\sim A=A\leftrightarrow \bigcup A/\sim A=A$$