Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
||
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 35980).
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 35994. Alternate definitions are dfdisjs 35975, ... , dfdisjs5 35979. (Contributed by Peter Mazsa, 17-Jul-2021.) |
Ref | Expression |
---|---|
df-disjs | ⊢ Disjs = ( Disjss ∩ Rels ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdisjs 35520 | . 2 class Disjs | |
2 | cdisjss 35519 | . . 3 class Disjss | |
3 | crels 35489 | . . 3 class Rels | |
4 | 2, 3 | cin 3928 | . 2 class ( Disjss ∩ Rels ) |
5 | 1, 4 | wceq 1536 | 1 wff Disjs = ( Disjss ∩ Rels ) |
Colors of variables: wff setvar class |
This definition is referenced by: dfdisjs 35975 |
Copyright terms: Public domain | W3C validator |