Definition df-coeleqvrels 38688

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 38698. Alternate definition is dfcoeleqvrels 38723. (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 38246	. 2 class CoElEqvRels
2		cep 5518	. . . . . . 7 class E
3	2	ccnv 5618	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1540	. . . . . 6 class 𝑎
6	3, 5	cres 5621	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38228	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38244	. . . 4 class EqvRels
9	7, 8	wcel 2111	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2709	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1541	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38697  dfcoeleqvrels  38723