Definition df-coeleqvrels 38840

Description: Define 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 38850. Alternate definition is dfcoeleqvrels 38875. (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 38371	. 2 class CoElEqvRels
2		cep 5522	. . . . . . 7 class E
3	2	ccnv 5622	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1541	. . . . . 6 class 𝑎
6	3, 5	cres 5625	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38353	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38369	. . . 4 class EqvRels
9	7, 8	wcel 2114	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2713	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1542	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38849  dfcoeleqvrels  38875