let V be non empty set ; :: thesis: for C being Category
for a being Object of C st Hom C c= V holds
(hom?? V,C) -? a = hom-? V,a
let C be Category; :: thesis: for a being Object of C st Hom C c= V holds
(hom?? V,C) -? a = hom-? V,a
let a be Object of C; :: thesis: ( Hom C c= V implies (hom?? V,C) -? a = hom-? V,a )
assume A1: Hom C c= V ; :: thesis: (hom?? V,C) -? a = hom-? V,a
hence (hom?? V,C) -? a = (curry' (hom?? C)) . (id a) by Def28
.= hom-? a by Th57
.= hom-? V,a by A1, Def27 ;
:: thesis: verum