Definition df-coeleqvrels 39522

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 39532. Alternate definition is dfcoeleqvrels 39557. (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 39053	. 2 class CoElEqvRels
2		cep 5546	. . . . . . 7 class E
3	2	ccnv 5646	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1569	. . . . . 6 class 𝑎
6	3, 5	cres 5649	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 39035	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 39051	. . . 4 class EqvRels
9	7, 8	wcel 2145	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2738	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1570	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is used by:  elcoeleqvrels  39531  dfcoeleqvrels  39557