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Definition df-coeleqvrel 37395
Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 37430. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 37404. (Contributed by Peter Mazsa, 11-Dec-2021.)
Assertion
Ref Expression
df-coeleqvrel ( CoElEqvRel 𝐴 ↔ EqvRel ≀ ( E ↾ 𝐴))

Detailed syntax breakdown of Definition df-coeleqvrel
StepHypRef Expression
1 cA . . 3 class 𝐴
21wcoeleqvrel 37000 . 2 wff CoElEqvRel 𝐴
3 cep 5578 . . . . . 6 class E
43ccnv 5674 . . . . 5 class E
54, 1cres 5677 . . . 4 class ( E ↾ 𝐴)
65ccoss 36981 . . 3 class ≀ ( E ↾ 𝐴)
76weqvrel 36998 . 2 wff EqvRel ≀ ( E ↾ 𝐴)
82, 7wb 205 1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ ( E ↾ 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  elcoeleqvrelsrel  37404  dfcoeleqvrel  37430  eqvreldmqs  37483  eldisjim  37592
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