Definition df-coeleqvrel 37761

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 37796. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 37770. (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 37366	. 2 wff CoElEqvRel 𝐴
3		cep 5580	. . . . . 6 class E
4	3	ccnv 5676	. . . . 5 class ◡ E
5	4, 1	cres 5679	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 37347	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 37364	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 205	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  37770  dfcoeleqvrel  37796  eqvreldmqs  37849  eldisjim  37958