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Definition df-eldisj 38708
Description: Define the disjoint element 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 38730.

As of now, disjoint elementhood is defined as "partition" in set.mm : compare df-prt 38873 with dfeldisj5 38722. See also the comments of dfmembpart2 38771 and of df-parts 38766. (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 38218 . 2 wff ElDisj 𝐴
3 cep 5583 . . . . 5 class E
43ccnv 5684 . . . 4 class E
54, 1cres 5687 . . 3 class ( E ↾ 𝐴)
65wdisjALTV 38216 . 2 wff Disj ( E ↾ 𝐴)
72, 6wb 206 1 wff ( ElDisj 𝐴 ↔ Disj ( E ↾ 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  dfeldisj2  38719  dfeldisj3  38720  dfeldisj4  38721  eleldisjseldisj  38730  eldisjss  38739  eldisjeq  38742  eldisjn0elb  38746  dfmembpart2  38771  eldisjim  38785  eldisjim2  38786  eldisjn0el  38807  eldisjlem19  38811  eqvreldisj3  38827
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