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 Th49:
  a is terminal implies for h being Morphism of a,a holds id a = h
proof
  assume a is terminal;
  then consider f being Morphism of a,a such that
A1: for g being Morphism of a,a holds f = g;
  let h be Morphism of a,a;
  id a = f by A1;
  hence thesis by A1;
end;
