Definition df-coeleqvrel 38922

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38957. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38931. (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 38453	. 2 wff CoElEqvRel 𝐴
3		cep 5531	. . . . . 6 class E
4	3	ccnv 5631	. . . . 5 class ◡ E
5	4, 1	cres 5634	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38434	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38451	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38931  dfcoeleqvrel  38957  eqvreldmqs  39011  eldisjim  39138