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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
StepHypRef Expression
1 ceqvrels 38198 . 2 class EqvRels
2 crefrels 38187 . . . 4 class RefRels
3 csymrels 38193 . . . 4 class SymRels
42, 3cin 3950 . . 3 class ( RefRels ∩ SymRels )
5 ctrrels 38196 . . 3 class TrRels
64, 5cin 3950 . 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
71, 6wceq 1540 1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )
Colors of variables: wff setvar class
This definition is referenced by:  dfeqvrels2  38589  refrelsredund2  38634
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