reserve x,y for Real,
  u,v,w for set,
  r for positive Real;

theorem
  for X being T_1 TopSpace st X is Tychonoff for B being prebasis of X
  for x being Point of X for V being Subset of X st x in V & V in B ex f being
  continuous Function of X, I[01] st f.x = 0 & f.:V` c= {1}
proof
  let X be T_1 TopSpace;
  assume
A1: X is Tychonoff;
  let B be prebasis of X;
  let x be Point of X;
  let V be Subset of X;
  assume that
A2: x in V and
A3: V in B;
A4: V`` = V;
  V is open by A3,TOPS_2:def 1;
  hence thesis by A4,A1,A2;
end;
