Definition df-coeleqvrels 39050

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 39060. Alternate definition is dfcoeleqvrels 39085. (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 38581	. 2 class CoElEqvRels
2		cep 5519	. . . . . . 7 class E
3	2	ccnv 5619	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1547	. . . . . 6 class 𝑎
6	3, 5	cres 5622	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38563	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38579	. . . 4 class EqvRels
9	7, 8	wcel 2121	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2719	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1548	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  39059  dfcoeleqvrels  39085