let C be Category; for f, g being Morphism of C holds [[(Hom ((cod f),(dom g))),(Hom ((dom f),(cod g)))],(hom (f,g))] is Element of Maps (Hom C)
let f, g be Morphism of C; [[(Hom ((cod f),(dom g))),(Hom ((dom f),(cod g)))],(hom (f,g))] is Element of Maps (Hom C)
A1:
( Hom ((dom f),(cod g)) in Hom C & Hom ((cod f),(dom g)) in Hom C )
;
( Hom ((dom f),(cod g)) = {} implies Hom ((cod f),(dom g)) = {} )
by Th50;
hence
[[(Hom ((cod f),(dom g))),(Hom ((dom f),(cod g)))],(hom (f,g))] is Element of Maps (Hom C)
by A1, Th5; verum