Metamath Proof Explorer


Definition df-disjss

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 }

Detailed syntax breakdown

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 }