Definition df-coeleqvrels 38568

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 38578. Alternate definition is dfcoeleqvrels 38603. (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 38180	. 2 class CoElEqvRels
2		cep 5588	. . . . . . 7 class E
3	2	ccnv 5688	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1536	. . . . . 6 class 𝑎
6	3, 5	cres 5691	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38162	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38178	. . . 4 class EqvRels
9	7, 8	wcel 2106	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2712	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1537	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38577  dfcoeleqvrels  38603