Definition df-coeleqvrel 38992

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39027. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39001. (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 38523	. 2 wff CoElEqvRel 𝐴
3		cep 5530	. . . . . 6 class E
4	3	ccnv 5630	. . . . 5 class ◡ E
5	4, 1	cres 5633	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38504	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38521	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  39001  dfcoeleqvrel  39027  eqvreldmqs  39081  eldisjim  39208