Definition df-coeleqvrels 39645

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 39655. Alternate definition is dfcoeleqvrels 39680. (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 39176	. 2 class CoElEqvRels
2		cep 5549	. . . . . . 7 class E
3	2	ccnv 5649	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1568	. . . . . 6 class 𝑎
6	3, 5	cres 5652	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 39158	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 39174	. . . 4 class EqvRels
9	7, 8	wcel 2144	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2738	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1569	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is used by:  elcoeleqvrels  39654  dfcoeleqvrels  39680