reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem Th47:
  for a,b being Object of c1Cat*(o,m), f being Morphism of c1Cat*(
  o,m) holds f in Hom(a,b)
proof
  let a,b be Object of c1Cat*(o,m), f be Morphism of c1Cat*(o,m);
  cod f = o by TARSKI:def 1;
  then
A1: cod f = b by TARSKI:def 1;
  dom f = o by TARSKI:def 1;
  then dom f = a by TARSKI:def 1;
  hence thesis by A1;
end;
