reserve C for CatStr;
reserve f,g for Morphism of C;
reserve C for non void non empty CatStr,
  f,g for Morphism of C,
  a,b,c,d for Object of C;
reserve o,m for set;
reserve B,C,D for Category;
reserve a,b,c,d for Object of C;
reserve f,f1,f2,g,g1,g2 for Morphism of C;
reserve f,f1,f2 for Morphism of a,b;
reserve f9 for Morphism of b,a;
reserve g for Morphism of b,c;
reserve h,h1,h2 for Morphism of c,d;

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;
