reserve i,j,k,n for Nat;

theorem
  for f being Function, y1,y2 being object st f is one-to-one & y1 in rng f
  & f"{y1} = f"{y2} holds y1 = y2
proof

  let f be Function, y1,y2 be object such that
A1: f is one-to-one & y1 in rng f and
A2: f"{y1} = f"{y2};
  consider x1 being object such that
A3: f"{y1} = {x1} by A1,FUNCT_1:74;
  f.x1 = y1 by A3,Th3;
  hence thesis by A2,A3,Th3;
end;
