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Definition df-coeleqvrel 36323
Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 36358. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 36332. (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 35975 . 2 wff CoElEqvRel 𝐴
3 cep 5433 . . . . . 6 class E
43ccnv 5524 . . . . 5 class E
54, 1cres 5527 . . . 4 class ( E ↾ 𝐴)
65ccoss 35956 . . 3 class ≀ ( E ↾ 𝐴)
76weqvrel 35973 . 2 wff EqvRel ≀ ( E ↾ 𝐴)
82, 7wb 209 1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ ( E ↾ 𝐴))
Colors of variables: wff setvar class
This definition is referenced by:  elcoeleqvrelsrel  36332  dfcoeleqvrel  36358  eqvreldmqs  36410
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