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Definition df-disjs 37877
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 37886).

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 37900. Alternate definitions are dfdisjs 37881, ... , dfdisjs5 37885. (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 37379 . 2 class Disjs
2 cdisjss 37378 . . 3 class Disjss
3 crels 37348 . . 3 class Rels
42, 3cin 3947 . 2 class ( Disjss ∩ Rels )
51, 4wceq 1541 1 wff Disjs = ( Disjss ∩ Rels )
Colors of variables: wff setvar class
This definition is referenced by:  dfdisjs  37881
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