Definition df-coeleqvrels 39347

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 39357. Alternate definition is dfcoeleqvrels 39382. (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 38878	. 2 class CoElEqvRels
2		cep 5559	. . . . . . 7 class E
3	2	ccnv 5659	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1568	. . . . . 6 class 𝑎
6	3, 5	cres 5662	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38860	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38876	. . . 4 class EqvRels
9	7, 8	wcel 2142	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2740	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1569	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is used by:  elcoeleqvrels  39356  dfcoeleqvrels  39382