Definition df-eqvrels 38690

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 38700. Alternate definitions are dfeqvrels2 38694 and dfeqvrels3 38695. (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 38248	. 2 class EqvRels
2		crefrels 38237	. . . 4 class RefRels
3		csymrels 38243	. . . 4 class SymRels
4	2, 3	cin 3896	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38246	. . 3 class TrRels
6	4, 5	cin 3896	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1541	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38694  refrelsredund2  38739