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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	$wff DomainQss = \{⟨x, y⟩ \| dom x / x = y\}$