Definition df-eqvrels 38607

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 38617. Alternate definitions are dfeqvrels2 38611 and dfeqvrels3 38612. (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 38220	. 2 class EqvRels
2		crefrels 38209	. . . 4 class RefRels
3		csymrels 38215	. . . 4 class SymRels
4	2, 3	cin 3930	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38218	. . 3 class TrRels
6	4, 5	cin 3930	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1540	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38611  refrelsredund2  38656