Definition df-coeleqvrel 38693

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38728. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38702. (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 38251	. 2 wff CoElEqvRel 𝐴
3		cep 5513	. . . . . 6 class E
4	3	ccnv 5613	. . . . 5 class ◡ E
5	4, 1	cres 5616	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38232	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38249	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38702  dfcoeleqvrel  38728  eqvreldmqs  38783  eldisjim  38892