Definition df-coeleqvrel 38854

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38889. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38863. (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 38402	. 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 38383	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38400	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38863  dfcoeleqvrel  38889  eqvreldmqs  38944  eldisjim  39053