Definition df-coeleqvrels 39405

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 39415. Alternate definition is dfcoeleqvrels 39440. (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 38936	. 2 class CoElEqvRels
2		cep 5558	. . . . . . 7 class E
3	2	ccnv 5658	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1569	. . . . . 6 class 𝑎
6	3, 5	cres 5661	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38918	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38934	. . . 4 class EqvRels
9	7, 8	wcel 2145	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2740	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1570	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is used by:  elcoeleqvrels  39414  dfcoeleqvrels  39440