let C be non empty non void CatStr ; :: thesis: 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; :: thesis: 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; :: thesis: ( Hom (a,b) <> {} implies ( dom f = a & cod f = b ) )
assume Hom (a,b) <> {} ; :: thesis: ( dom f = a & cod f = b )
then f in Hom (a,b) by Def3;
hence ( dom f = a & cod f = b ) by Th1; :: thesis: verum