Definition df-coeleqvrel 39210

Description: Define the coelement equivalence relation predicate. (Read: the coelement equivalence relation on 𝐴.) Alternate definition is dfcoeleqvrel 39245. For sets, being an element of the class of coelement equivalence relations is equivalent to satisfying the coelement equivalence relation predicate, see elcoeleqvrelsrel 39219. (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 38741	. 2 wff CoElEqvRel 𝐴
3		cep 5561	. . . . . 6 class E
4	3	ccnv 5661	. . . . 5 class ◡ E
5	4, 1	cres 5664	. . . 4 class (◡ E ↾ 𝐴)
6	5	ccoss 38722	. . 3 class ≀ (◡ E ↾ 𝐴)
7	6	weqvrel 38739	. 2 wff EqvRel ≀ (◡ E ↾ 𝐴)
8	2, 7	wb 209	1 wff ( CoElEqvRel 𝐴 ↔ EqvRel ≀ (◡ E ↾ 𝐴))

This definition is referenced by:  elcoeleqvrelsrel  39219  dfcoeleqvrel  39245  eqvreldmqs  39299  eldisjim  39426