Definition df-coeleqvrels 36678

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 36688. Alternate definition is dfcoeleqvrels 36713. (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 36330	. 2 class CoElEqvRels
2		cep 5493	. . . . . . 7 class E
3	2	ccnv 5587	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1540	. . . . . 6 class 𝑎
6	3, 5	cres 5590	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 36312	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 36328	. . . 4 class EqvRels
9	7, 8	wcel 2109	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2716	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1541	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  36687  dfcoeleqvrels  36713