Definition df-coeleqvrels 37946

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 37956. Alternate definition is dfcoeleqvrels 37981. (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 37551	. 2 class CoElEqvRels
2		cep 5569	. . . . . . 7 class E
3	2	ccnv 5665	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1532	. . . . . 6 class 𝑎
6	3, 5	cres 5668	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 37533	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 37549	. . . 4 class EqvRels
9	7, 8	wcel 2098	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2701	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1533	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  37955  dfcoeleqvrels  37981