Definition df-eqvrels 39419

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 39429. Alternate definitions are dfeqvrels2 39423 and dfeqvrels3 39424. (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 38950	. 2 class EqvRels
2		crefrels 38939	. . . 4 class RefRels
3		csymrels 38945	. . . 4 class SymRels
4	2, 3	cin 3898	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38948	. . 3 class TrRels
6	4, 5	cin 3898	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1570	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is used by:  dfeqvrels2  39423  refrelsredund2  39468