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Definition df-eldisj 35826
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 ∈ ElDisjs ↔ ElDisj 𝐴) when 𝐴 is a set, see eleldisjseldisj 35848.

As of now, disjoint elementhood is defined as "partition" in set.mm : compare df-prt 35894 with dfeldisj5 35840. See also the comments of ~? dfmembpart2 and of ~? df-parts . (Contributed by Peter Mazsa, 17-Jul-2021.)

Assertion
Ref Expression
df-eldisj ( ElDisj 𝐴 ↔ Disj ( E ↾ 𝐴))

Detailed syntax breakdown of Definition df-eldisj
StepHypRef Expression
1 cA . . 3 class 𝐴
21weldisj 35376 . 2 wff ElDisj 𝐴
3 cep 5463 . . . . 5 class E
43ccnv 5553 . . . 4 class E
54, 1cres 5556 . . 3 class ( E ↾ 𝐴)
65wdisjALTV 35374 . 2 wff Disj ( E ↾ 𝐴)
72, 6wb 207 1 wff ( ElDisj 𝐴 ↔ Disj ( E ↾ 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  dfeldisj2  35837  dfeldisj3  35838  dfeldisj4  35839  eleldisjseldisj  35848  eldisjss  35857  eldisjeq  35860
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