Definition df-coeleqvrel 39427

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39462. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39436. (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 38958	. 2 wff CoElEqvRel 𝐴
3		cep 5558	. . . . . 6 class E
4	3	ccnv 5658	. . . . 5 class ◡ E
5	4, 1	cres 5661	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38939	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38956	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is used by:  elcoeleqvrelsrel  39436  dfcoeleqvrel  39462  eqvreldmqs  39516  eldisjim  39643