Definition df-coeleqvrel 35865

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 35900. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 35874. (Contributed by Peter Mazsa, 11-Dec-2021.)

Assertion

Ref	Expression
df-coeleqvrel	⊢ ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

Detailed syntax breakdown of Definition df-coeleqvrel

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2	1	wcoeleqvrel 35515	. 2 wff CoElEqvRel 𝐴
3		cep 5457	. . . . . 6 class E
4	3	ccnv 5547	. . . . 5 class ◡ E
5	4, 1	cres 5550	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 35496	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 35513	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 208	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  35874  dfcoeleqvrel  35900  eqvreldmqs  35952