Definition df-eqvrels 38565

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 38575. Alternate definitions are dfeqvrels2 38569 and dfeqvrels3 38570. (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 38175	. 2 class EqvRels
2		crefrels 38164	. . . 4 class RefRels
3		csymrels 38170	. . . 4 class SymRels
4	2, 3	cin 3902	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38173	. . 3 class TrRels
6	4, 5	cin 3902	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1540	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38569  refrelsredund2  38614