Definition df-eqvrels 38585

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 38595. Alternate definitions are dfeqvrels2 38589 and dfeqvrels3 38590. (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 38198	. 2 class EqvRels
2		crefrels 38187	. . . 4 class RefRels
3		csymrels 38193	. . . 4 class SymRels
4	2, 3	cin 3950	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38196	. . 3 class TrRels
6	4, 5	cin 3950	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1540	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38589  refrelsredund2  38634