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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-disjs | Structured version Visualization version GIF version |
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 35490).
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 35504. Alternate definitions are dfdisjs 35485, ... , dfdisjs5 35489. (Contributed by Peter Mazsa, 17-Jul-2021.) |
Ref | Expression |
---|---|
df-disjs | ⊢ Disjs = ( Disjss ∩ Rels ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdisjs 35031 | . 2 class Disjs | |
2 | cdisjss 35030 | . . 3 class Disjss | |
3 | crels 35000 | . . 3 class Rels | |
4 | 2, 3 | cin 3860 | . 2 class ( Disjss ∩ Rels ) |
5 | 1, 4 | wceq 1522 | 1 wff Disjs = ( Disjss ∩ Rels ) |
Colors of variables: wff setvar class |
This definition is referenced by: dfdisjs 35485 |
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