Definition df-coeleqvrel 38610

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 38645. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 38619. (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 38223	. 2 wff CoElEqvRel 𝐴
3		cep 5557	. . . . . 6 class E
4	3	ccnv 5658	. . . . 5 class ◡ E
5	4, 1	cres 5661	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38204	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38221	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 206	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  38619  dfcoeleqvrel  38645  eqvreldmqs  38698  eldisjim  38807