Definition df-coeleqvrel 39743

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39778. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39752. (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 39274	. 2 wff CoElEqvRel 𝐴
3		cep 5553	. . . . . 6 class E
4	3	ccnv 5653	. . . . 5 class ◡ E
5	4, 1	cres 5656	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 39255	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 39272	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is used by:  elcoeleqvrelsrel  39752  dfcoeleqvrel  39778  eqvreldmqs  39832  eldisjim  39959