Definition df-eqvrels 38566

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 38576. Alternate definitions are dfeqvrels2 38570 and dfeqvrels3 38571. (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 38178	. 2 class EqvRels
2		crefrels 38167	. . . 4 class RefRels
3		csymrels 38173	. . . 4 class SymRels
4	2, 3	cin 3962	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38176	. . 3 class TrRels
6	4, 5	cin 3962	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1537	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38570  refrelsredund2  38615