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Definition df-eqvrels 36461
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 36471. Alternate definitions are dfeqvrels2 36465 and dfeqvrels3 36466. (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 36113 . 2 class EqvRels
2 crefrels 36102 . . . 4 class RefRels
3 csymrels 36108 . . . 4 class SymRels
42, 3cin 3880 . . 3 class ( RefRels ∩ SymRels )
5 ctrrels 36111 . . 3 class TrRels
64, 5cin 3880 . 2 class (( RefRels ∩ SymRels ) ∩ TrRels )
71, 6wceq 1543 1 wff EqvRels = (( RefRels ∩ SymRels ) ∩ TrRels )
Colors of variables: wff setvar class
This definition is referenced by:  dfeqvrels2  36465  refrelsredund2  36510
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