Definition df-disjs 37239

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 37248).

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 37262. Alternate definitions are dfdisjs 37243, ... , dfdisjs5 37247. (Contributed by Peter Mazsa, 17-Jul-2021.)

Assertion

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

Detailed syntax breakdown of Definition df-disjs

Step	Hyp	Ref	Expression
1		cdisjs 36740	. 2 class Disjs
2		cdisjss 36739	. . 3 class Disjss
3		crels 36709	. . 3 class Rels
4	2, 3	cin 3912	. 2 class ( Disjss ∩ Rels )
5	1, 4	wceq 1541	1 wff Disjs = ( Disjss ∩ Rels )

This definition is referenced by:  dfdisjs  37243