Definition df-coeleqvrel 39603

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39638. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39612. (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 39134	. 2 wff CoElEqvRel 𝐴
3		cep 5550	. . . . . 6 class E
4	3	ccnv 5650	. . . . 5 class ◡ E
5	4, 1	cres 5653	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 39115	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 39132	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is used by:  elcoeleqvrelsrel  39612  dfcoeleqvrel  39638  eqvreldmqs  39692  eldisjim  39819