theorem
 for a,b being Element of C st Hom(a,b)<>{}
  ex m being Morphism of a,b st m in Hom(a,b)
proof let a,b being Element of C;
 assume Hom(a,b)<>{};
  then consider m being object such that
A1: m in Hom(a,b) by XBOOLE_0:def 1;
  reconsider m as Morphism of a,b by A1,Def3;
 take m;
 thus thesis by A1;
end;
