Definition df-coeleqvrels 38988

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 38998. Alternate definition is dfcoeleqvrels 39023. (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 38519	. 2 class CoElEqvRels
2		cep 5527	. . . . . . 7 class E
3	2	ccnv 5627	. . . . . 6 class ◡ E
4		va	. . . . . . 7 setvar 𝑎
5	4	cv 1541	. . . . . 6 class 𝑎
6	3, 5	cres 5630	. . . . 5 class (◡ E ↾ 𝑎)
7	6	ccoss 38501	. . . 4 class ≀ (◡ E ↾ 𝑎)
8		ceqvrels 38517	. . . 4 class EqvRels
9	7, 8	wcel 2114	. . 3 wff ≀ (◡ E ↾ 𝑎) ∈ EqvRels
10	9, 4	cab 2715	. 2 class {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }
11	1, 10	wceq 1542	1 wff CoElEqvRels = {𝑎 ∣ ≀ (◡ E ↾ 𝑎) ∈ EqvRels }

This definition is referenced by:  elcoeleqvrels  38997  dfcoeleqvrels  39023