Description: Define the disjoint elementhood relation predicate, i.e., the disjoint elementhood predicate. Read: the elements of A are disjoint. The element of the disjoint elements class and the disjoint elementhood predicate are the same, that is ( A e. ElDisjs <-> ElDisj A ) when A is a set, see eleldisjseldisj .
As of now, disjoint elementhood is defined as "partition" in set.mm : compare df-prt with dfeldisj5 . See also the comments of ~? dfmembpart2 and of ~? df-parts . (Contributed by Peter Mazsa, 17-Jul-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | df-eldisj |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | cA | ||
1 | 0 | weldisj | |
2 | cep | ||
3 | 2 | ccnv | |
4 | 3 0 | cres | |
5 | 4 | wdisjALTV | |
6 | 1 5 | wb |