Definition df-eqvrels 38575

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 38585. Alternate definitions are dfeqvrels2 38579 and dfeqvrels3 38580. (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 38185	. 2 class EqvRels
2		crefrels 38174	. . . 4 class RefRels
3		csymrels 38180	. . . 4 class SymRels
4	2, 3	cin 3913	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38183	. . 3 class TrRels
6	4, 5	cin 3913	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1540	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38579  refrelsredund2  38624