Definition df-coeleqvrel 37395

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 37430. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 37404. (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 37000	. 2 wff CoElEqvRel 𝐴
3		cep 5578	. . . . . 6 class E
4	3	ccnv 5674	. . . . 5 class ◡ E
5	4, 1	cres 5677	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 36981	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 36998	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 205	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  37404  dfcoeleqvrel  37430  eqvreldmqs  37483  eldisjim  37592