reserve a,x,y for object, A,B for set,
  l,m,n for Nat;

theorem Th3:
  for X,Y be non empty set, f being Function of X,Y st f is
one-to-one for x being Element of X, A being Subset of X st f.x in f.:A holds x
  in A
proof
  let X,Y be non empty set, f be Function of X,Y such that
A1: f is one-to-one;
  let x be Element of X, A be Subset of X;
  assume f.x in f.:A;
  then ex y be Element of X st y in A & f.y = f.x by FUNCT_2:65;
  hence thesis by A1,FUNCT_2:19;
end;
