Metamath Proof Explorer


Definition df-dmqss

Description: Define the class of domain quotients. Domain quotients are pairs of sets, typically a relation and a set, where the quotient (see df-qs ) of the relation on its domain is equal to the set. See comments of df-ers for the motivation for this definition. (Contributed by Peter Mazsa, 16-Apr-2019)

Ref Expression
Assertion df-dmqss DomainQss = x y | dom x / x = y

Detailed syntax breakdown

Step Hyp Ref Expression
0 cdmqss class DomainQss
1 vx setvar x
2 vy setvar y
3 1 cv setvar x
4 3 cdm class dom x
5 4 3 cqs class dom x / x
6 2 cv setvar y
7 5 6 wceq wff dom x / x = y
8 7 1 2 copab class x y | dom x / x = y
9 0 8 wceq wff DomainQss = x y | dom x / x = y