Definition df-coeleqvrel 39009

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39044. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39018. (Contributed by Peter Mazsa, 11-Dec-2021.)

Assertion

Ref	Expression
df-coeleqvrel	⊢ ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

Detailed syntax breakdown of Definition df-coeleqvrel

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2	1	wcoeleqvrel 38540	. 2 wff CoElEqvRel 𝐴
3		cep 5524	. . . . . 6 class E
4	3	ccnv 5624	. . . . 5 class ◡ E
5	4, 1	cres 5627	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38521	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38538	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  39018  dfcoeleqvrel  39044  eqvreldmqs  39098  eldisjim  39225