Definition df-coeleqvrels 39265

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 39275. Alternate definition is dfcoeleqvrels 39300. (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 38796	. 2 class CoElEqvRels
2		cep 5560	. . . . . . 7 class E
3	2	ccnv 5660	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1567	. . . . . 6 class 𝑎
6	3, 5	cres 5663	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38778	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38794	. . . 4 class EqvRels
9	7, 8	wcel 2141	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2739	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1568	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  39274  dfcoeleqvrels  39300