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 )