Definition df-coeleqvrels 38982

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 38992. Alternate definition is dfcoeleqvrels 39017. (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 38513	. 2 class CoElEqvRels
2		cep 5521	. . . . . . 7 class E
3	2	ccnv 5621	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1541	. . . . . 6 class 𝑎
6	3, 5	cres 5624	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38495	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38511	. . . 4 class EqvRels
9	7, 8	wcel 2114	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2715	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1542	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38991  dfcoeleqvrels  39017