Definition df-coeleqvrel 39038

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39073. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39047. (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 38569	. 2 wff CoElEqvRel 𝐴
3		cep 5517	. . . . . 6 class E
4	3	ccnv 5617	. . . . 5 class ◡ E
5	4, 1	cres 5620	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38550	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38567	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 207	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  39047  dfcoeleqvrel  39073  eqvreldmqs  39127  eldisjim  39254