Definition df-coeleqvrels 39794

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 39804. Alternate definition is dfcoeleqvrels 39829. (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 39325	. 2 class CoElEqvRels
2		cep 5554	. . . . . . 7 class E
3	2	ccnv 5654	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1569	. . . . . 6 class 𝑎
6	3, 5	cres 5657	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 39307	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 39323	. . . 4 class EqvRels
9	7, 8	wcel 2147	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2741	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1570	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is used by:  elcoeleqvrels  39803  dfcoeleqvrels  39829