Definition df-coeleqvrel 39006

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39041. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39015. (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 38537	. 2 wff CoElEqvRel 𝐴
3		cep 5523	. . . . . 6 class E
4	3	ccnv 5623	. . . . 5 class ◡ E
5	4, 1	cres 5626	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38518	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38535	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  39015  dfcoeleqvrel  39041  eqvreldmqs  39095  eldisjim  39222