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Definition df-eldisj 37515
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 37537.

As of now, disjoint elementhood is defined as "partition" in set.mm : compare df-prt 37680 with dfeldisj5 37529. See also the comments of dfmembpart2 37578 and of df-parts 37573. (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 37017 . 2 wff ElDisj 𝐴
3 cep 5578 . . . . 5 class E
43ccnv 5674 . . . 4 class E
54, 1cres 5677 . . 3 class ( E ↾ 𝐴)
65wdisjALTV 37015 . 2 wff Disj ( E ↾ 𝐴)
72, 6wb 205 1 wff ( ElDisj 𝐴 ↔ Disj ( E ↾ 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  dfeldisj2  37526  dfeldisj3  37527  dfeldisj4  37528  eleldisjseldisj  37537  eldisjss  37546  eldisjeq  37549  eldisjn0elb  37553  dfmembpart2  37578  eldisjim  37592  eldisjim2  37593  eldisjn0el  37614  eldisjlem19  37618  eqvreldisj3  37634
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