Definition df-eqvrels 36697

Description: Define the class of equivalence relations. For sets, being an element of the class of equivalence relations is equivalent to satisfying the equivalence relation predicate, see eleqvrelsrel 36707. Alternate definitions are dfeqvrels2 36701 and dfeqvrels3 36702. (Contributed by Peter Mazsa, 7-Nov-2018.)

Assertion

Ref	Expression
df-eqvrels	⊢ EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

Detailed syntax breakdown of Definition df-eqvrels

Step	Hyp	Ref	Expression
1		ceqvrels 36349	. 2 class EqvRels
2		crefrels 36338	. . . 4 class RefRels
3		csymrels 36344	. . . 4 class SymRels
4	2, 3	cin 3886	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 36347	. . 3 class TrRels
6	4, 5	cin 3886	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1539	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  36701  refrelsredund2  36746