Description: Define the class of all disjoint sets (but not necessarily disjoint relations, cf. df-disjs ). It is used only by df-disjs . (Contributed by Peter Mazsa, 17-Jul-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | df-disjss | |- Disjss = { x | ,~ `' x e. CnvRefRels } |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | cdisjss | |- Disjss |
|
1 | vx | |- x |
|
2 | 1 | cv | |- x |
3 | 2 | ccnv | |- `' x |
4 | 3 | ccoss | |- ,~ `' x |
5 | ccnvrefrels | |- CnvRefRels |
|
6 | 4 5 | wcel | |- ,~ `' x e. CnvRefRels |
7 | 6 1 | cab | |- { x | ,~ `' x e. CnvRefRels } |
8 | 0 7 | wceq | |- Disjss = { x | ,~ `' x e. CnvRefRels } |