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Definition df-coeleqvrel 36700
Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 36735. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 36709. (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 36352 . 2 wff CoElEqvRel 𝐴
3 cep 5494 . . . . . 6 class E
43ccnv 5588 . . . . 5 class E
54, 1cres 5591 . . . 4 class ( E ↾ 𝐴)
65ccoss 36333 . . 3 class ≀ ( E ↾ 𝐴)
76weqvrel 36350 . 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  36709  dfcoeleqvrel  36735  eqvreldmqs  36787
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