Definition df-coeleqvrels 38583

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 38593. Alternate definition is dfcoeleqvrels 38618. (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 38193	. 2 class CoElEqvRels
2		cep 5518	. . . . . . 7 class E
3	2	ccnv 5618	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1539	. . . . . 6 class 𝑎
6	3, 5	cres 5621	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38175	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38191	. . . 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  38592  dfcoeleqvrels  38618