Definition df-coeleqvrel 36627

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 36662. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 36636. (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 36279	. 2 wff CoElEqvRel 𝐴
3		cep 5485	. . . . . 6 class E
4	3	ccnv 5579	. . . . 5 class ◡ E
5	4, 1	cres 5582	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 36260	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 36277	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 205	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  36636  dfcoeleqvrel  36662  eqvreldmqs  36714