Definition df-coeleqvrel 38588

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38623. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38597. (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 38201	. 2 wff CoElEqvRel 𝐴
3		cep 5583	. . . . . 6 class E
4	3	ccnv 5684	. . . . 5 class ◡ E
5	4, 1	cres 5687	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38182	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38199	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38597  dfcoeleqvrel  38623  eqvreldmqs  38676  eldisjim  38785