
theorem
  for X being non empty set, x,y being object st X --> x = X --> y holds x = y
proof
  let X be non empty set, x,y be object;
  assume A1: X --> x = X --> y;
  rng(X --> x) = {x} & rng(X --> y) = {y} by FUNCOP_1:8;
  hence thesis by A1, ZFMISC_1:3;
end;
