reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;

theorem Th65:
  for f being set st f in Funcs(X,Y) holds f is Function of X,Y
proof
  let f be set;
  assume f in Funcs(X,Y);
  then
  ( not(Y = {} & X <> {}))& ex f9 being Function st f9 = f & dom f9 = X &
  rng f9 c= Y by Def2;
  hence thesis by Def1,RELSET_1:4;
end;
