Definition df-coeleqvrels 38609

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 38619. Alternate definition is dfcoeleqvrels 38644. (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 38222	. 2 class CoElEqvRels
2		cep 5557	. . . . . . 7 class E
3	2	ccnv 5658	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1539	. . . . . 6 class 𝑎
6	3, 5	cres 5661	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38204	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38220	. . . 4 class EqvRels
9	7, 8	wcel 2109	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2714	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1540	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38618  dfcoeleqvrels  38644