Definition df-coeleqvrel 37122

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 37157. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 37131. (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 36726	. 2 wff CoElEqvRel 𝐴
3		cep 5541	. . . . . 6 class E
4	3	ccnv 5637	. . . . 5 class ◡ E
5	4, 1	cres 5640	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 36707	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 36724	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 205	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  37131  dfcoeleqvrel  37157  eqvreldmqs  37210  eldisjim  37319