Definition df-coeleqvrel 39422

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39457. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39431. (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 38953	. 2 wff CoElEqvRel 𝐴
3		cep 5554	. . . . . 6 class E
4	3	ccnv 5654	. . . . 5 class ◡ E
5	4, 1	cres 5657	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38934	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38951	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is used by:  elcoeleqvrelsrel  39431  dfcoeleqvrel  39457  eqvreldmqs  39511  eldisjim  39638