
theorem
  for T being TopStruct, x, y being Point of T, Y, V being Subset of T
  st Y = {y} & x in Cl Y & V is open & x in V holds y in V
proof
  let T be TopStruct, x, y be Point of T, Y, V be Subset of T such that
A1: Y = {y};
  assume x in Cl Y & V is open & x in V;
  then Y meets V by PRE_TOPC:def 7;
  hence thesis by A1,ZFMISC_1:50;
end;
