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Definition df-disjs 38705
Description: Define the disjoint relations class, i.e., the class of disjoints. We need Disjs for the definition of Parts and Part for the Partition-Equivalence Theorems: this need for Parts as disjoint relations on their domain quotients is the reason why we must define Disjs instead of simply using converse functions (cf. dfdisjALTV 38714).

The element of the class of disjoints and the disjoint predicate are the same, that is (𝑅 ∈ Disjs ↔ Disj 𝑅) when 𝑅 is a set, see eldisjsdisj 38728. Alternate definitions are dfdisjs 38709, ... , dfdisjs5 38713. (Contributed by Peter Mazsa, 17-Jul-2021.)

Assertion
Ref Expression
df-disjs Disjs = ( Disjss ∩ Rels )

Detailed syntax breakdown of Definition df-disjs
StepHypRef Expression
1 cdisjs 38215 . 2 class Disjs
2 cdisjss 38214 . . 3 class Disjss
3 crels 38184 . . 3 class Rels
42, 3cin 3950 . 2 class ( Disjss ∩ Rels )
51, 4wceq 1540 1 wff Disjs = ( Disjss ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfdisjs  38709
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