Definition df-coeleqvrel 36700

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 36735. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 36709. (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 36352	. 2 wff CoElEqvRel 𝐴
3		cep 5494	. . . . . 6 class E
4	3	ccnv 5588	. . . . 5 class ◡ E
5	4, 1	cres 5591	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 36333	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 36350	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 205	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  36709  dfcoeleqvrel  36735  eqvreldmqs  36787