
theorem Th22:
  for T being non empty TopSpace, p being Point of T for A, B
  being Element of OpenNeighborhoods p holds A /\ B is Element of
  OpenNeighborhoods p
proof
  let T be non empty TopSpace, p be Point of T, A, B be Element of
  OpenNeighborhoods p;
  consider W being Subset of T such that
A1: W = A and
A2: p in W & W is open by YELLOW_6:29;
  consider X being Subset of T such that
A3: X = B and
A4: p in X & X is open by YELLOW_6:29;
  p in A /\ B & W /\ X is open by A1,A2,A3,A4,XBOOLE_0:def 4;
  hence thesis by A1,A3,YELLOW_6:30;
end;
