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 Th23:
  Hom(a,b)<>{} implies (id b)*f=f
proof
  assume
A1: Hom(a,b)<>{};
A2: (id b)(*)f = f by A1,Def10;
  Hom(b,b) <> {};
  hence thesis by A1,A2,Def11;
end;
