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Metamath Proof Explorer

Definition df-dmqs

Description: Define the domain quotient predicate. (Read: the domain quotient of R is A .) If A and R are sets, the domain quotient binary relation and the domain quotient predicate are the same, see brdmqssqs . (Contributed by Peter Mazsa, 9-Aug-2021)

		Ref	Expression
	Assertion	df-dmqs	\|- ( R DomainQs A <-> ( dom R /. R ) = A )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cR	\|- R
1		cA	\|- A
2	1 0	wdmqs	\|- R DomainQs A
3	0	cdm	\|- dom R
4	3 0	cqs	\|- ( dom R /. R )
5	4 1	wceq	\|- ( dom R /. R ) = A
6	2 5	wb	\|- ( R DomainQs A <-> ( dom R /. R ) = A )