Definition df-coeleqvrels 38570

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 38580. Alternate definition is dfcoeleqvrels 38605. (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 38180	. 2 class CoElEqvRels
2		cep 5530	. . . . . . 7 class E
3	2	ccnv 5630	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1539	. . . . . 6 class 𝑎
6	3, 5	cres 5633	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38162	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38178	. . . 4 class EqvRels
9	7, 8	wcel 2109	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2707	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1540	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38579  dfcoeleqvrels  38605