Definition df-eqvrels 38919

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 38929. Alternate definitions are dfeqvrels2 38923 and dfeqvrels3 38924. (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 38450	. 2 class EqvRels
2		crefrels 38439	. . . 4 class RefRels
3		csymrels 38445	. . . 4 class SymRels
4	2, 3	cin 3902	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38448	. . 3 class TrRels
6	4, 5	cin 3902	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1542	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38923  refrelsredund2  38968