Definition df-coeleqvrel 38783

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38818. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38792. (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 38341	. 2 wff CoElEqvRel 𝐴
3		cep 5521	. . . . . 6 class E
4	3	ccnv 5621	. . . . 5 class ◡ E
5	4, 1	cres 5624	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38322	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38339	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38792  dfcoeleqvrel  38818  eqvreldmqs  38873  eldisjim  38982