Definition df-coeleqvrels 36800

Description: Define the 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 36810. Alternate definition is dfcoeleqvrels 36835. (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 36399	. 2 class CoElEqvRels
2		cep 5505	. . . . . . 7 class E
3	2	ccnv 5599	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1538	. . . . . 6 class 𝑎
6	3, 5	cres 5602	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 36381	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 36397	. . . 4 class EqvRels
9	7, 8	wcel 2104	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2713	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1539	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  36809  dfcoeleqvrels  36835