
theorem Th2:
  for F being non empty functional set, x,y be set, g being Element
  of F holds g in F\(x,y) iff g.x <> y
proof
  let F be non empty functional set;
  let x,y be set;
  let g be Element of F;
  g in F\(x,y) iff ex f being Element of F st g = f & f.x <> y;
  hence thesis;
end;
