Definition df-eqvrels 39600

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 39610. Alternate definitions are dfeqvrels2 39604 and dfeqvrels3 39605. (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 39131	. 2 class EqvRels
2		crefrels 39120	. . . 4 class RefRels
3		csymrels 39126	. . . 4 class SymRels
4	2, 3	cin 3898	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 39129	. . 3 class TrRels
6	4, 5	cin 3898	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1570	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is used by:  dfeqvrels2  39604  refrelsredund2  39649