Definition df-coeleqvrel 39380

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39415. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39389. (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 38911	. 2 wff CoElEqvRel 𝐴
3		cep 5562	. . . . . 6 class E
4	3	ccnv 5662	. . . . 5 class ◡ E
5	4, 1	cres 5665	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38892	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38909	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is used by:  elcoeleqvrelsrel  39389  dfcoeleqvrel  39415  eqvreldmqs  39469  eldisjim  39596