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Definition df-disjs 36096
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 36105).

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 36119. Alternate definitions are dfdisjs 36100, ... , dfdisjs5 36104. (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 35645 . 2 class Disjs
2 cdisjss 35644 . . 3 class Disjss
3 crels 35614 . . 3 class Rels
42, 3cin 3883 . 2 class ( Disjss ∩ Rels )
51, 4wceq 1538 1 wff Disjs = ( Disjss ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfdisjs  36100
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