Definition df-coeleqvrel 38571

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38606. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38580. (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 38181	. 2 wff CoElEqvRel 𝐴
3		cep 5530	. . . . . 6 class E
4	3	ccnv 5630	. . . . 5 class ◡ E
5	4, 1	cres 5633	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38162	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38179	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38580  dfcoeleqvrel  38606  eqvreldmqs  38660  eldisjim  38769