Definition df-coeleqvrels 38542

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 38552. Alternate definition is dfcoeleqvrels 38577. (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 38153	. 2 class CoElEqvRels
2		cep 5598	. . . . . . 7 class E
3	2	ccnv 5699	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1536	. . . . . 6 class 𝑎
6	3, 5	cres 5702	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38135	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38151	. . . 4 class EqvRels
9	7, 8	wcel 2108	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2717	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1537	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38551  dfcoeleqvrels  38577