
theorem Th20:
  for C being non empty with_identities composable CategoryStr,
      a,b being Object of C, f being morphism of C holds
      f in Hom(a,b) iff dom f = a & cod f = b
  proof
    let C be non empty with_identities composable CategoryStr;
    let a,b be Object of C;
    let f be morphism of C;
    hereby
      assume f in Hom(a,b);
      then consider f1 be morphism of C such that
A1:   f = f1 & a = dom f1 & b = cod f1;
      thus dom f = a & cod f = b by A1;
    end;
    assume dom f = a & cod f = b;
    hence f in Hom(a,b);
  end;
