Definition df-coeleqvrel 38568

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38603. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38577. (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 38178	. 2 wff CoElEqvRel 𝐴
3		cep 5518	. . . . . 6 class E
4	3	ccnv 5618	. . . . 5 class ◡ E
5	4, 1	cres 5621	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38159	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38176	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38577  dfcoeleqvrel  38603  eqvreldmqs  38657  eldisjim  38766