Definition df-coeleqvrel 39340

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39375. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39349. (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 38871	. 2 wff CoElEqvRel 𝐴
3		cep 5560	. . . . . 6 class E
4	3	ccnv 5660	. . . . 5 class ◡ E
5	4, 1	cres 5663	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38852	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38869	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  39349  dfcoeleqvrel  39375  eqvreldmqs  39429  eldisjim  39556