Definition df-coeleqvrels 35864

Description: Define the the coelement equivalence relations class, the class of sets with coelement equivalence relations. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 35874. Alternate definition is dfcoeleqvrels 35899. (Contributed by Peter Mazsa, 28-Nov-2022.)

Assertion

Ref	Expression
df-coeleqvrels	⊢ CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

Detailed syntax breakdown of Definition df-coeleqvrels

Step	Hyp	Ref	Expression
1		ccoeleqvrels 35514	. 2 class CoElEqvRels
2		cep 5457	. . . . . . 7 class E
3	2	ccnv 5547	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1535	. . . . . 6 class 𝑎
6	3, 5	cres 5550	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 35496	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 35512	. . . 4 class EqvRels
9	7, 8	wcel 2113	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2798	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1536	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  35873  dfcoeleqvrels  35899