Definition df-coeleqvrel 36323

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 36358. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 36332. (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 35975	. 2 wff CoElEqvRel 𝐴
3		cep 5433	. . . . . 6 class E
4	3	ccnv 5524	. . . . 5 class ◡ E
5	4, 1	cres 5527	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 35956	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 35973	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  36332  dfcoeleqvrel  36358  eqvreldmqs  36410