Definition df-coeleqvrels 35853

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 35863. Alternate definition is dfcoeleqvrels 35888. (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 35503	. 2 class CoElEqvRels
2		cep 5450	. . . . . . 7 class E
3	2	ccnv 5540	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1536	. . . . . 6 class 𝑎
6	3, 5	cres 5543	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 35485	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 35501	. . . 4 class EqvRels
9	7, 8	wcel 2114	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2799	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1537	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  35862  dfcoeleqvrels  35888