let V be non empty set ; :: thesis: for C being Category
for a, b being Object of C st Hom C c= V holds
(Obj (hom?- V,a)) . b = Hom a,b
let C be Category; :: thesis: for a, b being Object of C st Hom C c= V holds
(Obj (hom?- V,a)) . b = Hom a,b
let a, b be Object of C; :: thesis: ( Hom C c= V implies (Obj (hom?- V,a)) . b = Hom a,b )
assume A1: Hom C c= V ; :: thesis: (Obj (hom?- V,a)) . b = Hom a,b
Hom a,b in Hom C ;
then reconsider A = Hom a,b as Element of V by A1;
set d = @ A;
(hom?- V,a) . (id b) = (hom?- a) . (id b) by A1, Def26
.= id (@ A) by A1, Lm8 ;
hence (Obj (hom?- V,a)) . b = Hom a,b by CAT_1:103; :: thesis: verum