Definition df-coeleqvrels 38369

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 38379. Alternate definition is dfcoeleqvrels 38404. (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 37979	. 2 class CoElEqvRels
2		cep 5587	. . . . . . 7 class E
3	2	ccnv 5683	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1533	. . . . . 6 class 𝑎
6	3, 5	cres 5686	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 37961	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 37977	. . . 4 class EqvRels
9	7, 8	wcel 2100	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2706	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1534	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38378  dfcoeleqvrels  38404