Definition df-coeleqvrels 38979

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 38989. Alternate definition is dfcoeleqvrels 39014. (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 38510	. 2 class CoElEqvRels
2		cep 5519	. . . . . . 7 class E
3	2	ccnv 5619	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1541	. . . . . 6 class 𝑎
6	3, 5	cres 5622	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38492	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38508	. . . 4 class EqvRels
9	7, 8	wcel 2114	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2713	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1542	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38988  dfcoeleqvrels  39014