Definition df-coeleqvrels 38577

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 38587. Alternate definition is dfcoeleqvrels 38612. (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 38187	. 2 class CoElEqvRels
2		cep 5537	. . . . . . 7 class E
3	2	ccnv 5637	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1539	. . . . . 6 class 𝑎
6	3, 5	cres 5640	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38169	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38185	. . . 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  38586  dfcoeleqvrels  38612