let C be non empty non void CatStr ; for a, b being Object of C
for f being Morphism of a,b st Hom (a,b) <> {} holds
( dom f = a & cod f = b )
let a, b be Object of C; for f being Morphism of a,b st Hom (a,b) <> {} holds
( dom f = a & cod f = b )
let f be Morphism of a,b; ( Hom (a,b) <> {} implies ( dom f = a & cod f = b ) )
assume
Hom (a,b) <> {}
; ( dom f = a & cod f = b )
then
f in Hom (a,b)
by Def3;
hence
( dom f = a & cod f = b )
by Th1; verum