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Definition df-coeleqvrel 38588
Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38623. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38597. (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 38201 . 2 wff CoElEqvRel 𝐴
3 cep 5583 . . . . . 6 class E
43ccnv 5684 . . . . 5 class E
54, 1cres 5687 . . . 4 class ( E ↾ 𝐴)
65ccoss 38182 . . 3 class ≀ ( E ↾ 𝐴)
76weqvrel 38199 . 2 wff EqvRel ≀ ( E ↾ 𝐴)
82, 7wb 206 1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ ( E ↾ 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  elcoeleqvrelsrel  38597  dfcoeleqvrel  38623  eqvreldmqs  38676  eldisjim  38785
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