Definition df-coeleqvrel 39869

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39904. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39878. (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 39400	. 2 wff CoElEqvRel 𝐴
3		cep 5557	. . . . . 6 class E
4	3	ccnv 5657	. . . . 5 class ◡ E
5	4, 1	cres 5660	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 39381	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 39398	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is used by:  elcoeleqvrelsrel  39878  dfcoeleqvrel  39904  eqvreldmqs  39958  eldisjim  40085