Definition df-coeleqvrels 39174

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 39184. Alternate definition is dfcoeleqvrels 39209. (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 38705	. 2 class CoElEqvRels
2		cep 5548	. . . . . . 7 class E
3	2	ccnv 5648	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1561	. . . . . 6 class 𝑎
6	3, 5	cres 5651	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38687	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38703	. . . 4 class EqvRels
9	7, 8	wcel 2144	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2742	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1562	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  39183  dfcoeleqvrels  39209