
theorem
  for f being one-to-one Function, y being object st rng f = {y}
  ex x being object st f = x .--> y
proof
  let f be one-to-one Function, y be object;
  assume A1: rng f = {y};
  then y in rng f by TARSKI:def 1;
  then consider x being object such that
    A2: x in dom f & f.x = y by FUNCT_1:def 3;
  take x;
  f is constant by A1;
  then dom f = {x} by A2, ZFMISC_1:132;
  hence thesis by A1, FUNCT_4:112;
end;
