Definition df-eqvrels 38780

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 38790. Alternate definitions are dfeqvrels2 38784 and dfeqvrels3 38785. (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 38338	. 2 class EqvRels
2		crefrels 38327	. . . 4 class RefRels
3		csymrels 38333	. . . 4 class SymRels
4	2, 3	cin 3898	. . 3 class ( RefRels ∩ SymRels )
5		ctrrels 38336	. . 3 class TrRels
6	4, 5	cin 3898	. 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
7	1, 6	wceq 1541	1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )

This definition is referenced by:  dfeqvrels2  38784  refrelsredund2  38829