Definition df-coeleqvrels 37247

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 37257. Alternate definition is dfcoeleqvrels 37282. (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 36852	. 2 class CoElEqvRels
2		cep 5571	. . . . . . 7 class E
3	2	ccnv 5667	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1540	. . . . . 6 class 𝑎
6	3, 5	cres 5670	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 36834	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 36850	. . . 4 class EqvRels
9	7, 8	wcel 2106	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2708	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1541	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  37256  dfcoeleqvrels  37282