Definition df-coeleqvrel 39170

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39205. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39179. (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 38701	. 2 wff CoElEqvRel 𝐴
3		cep 5546	. . . . . 6 class E
4	3	ccnv 5646	. . . . 5 class ◡ E
5	4, 1	cres 5649	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38682	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38699	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 208	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  39179  dfcoeleqvrel  39205  eqvreldmqs  39259  eldisjim  39386