reserve x,X,X2,Y,Y2 for set;
reserve GX for non empty TopSpace;
reserve A2,B2 for Subset of GX;
reserve B for Subset of GX;

theorem
  for B being Subset of GX, p be Point of GX st p in B holds p in
  Component_of(p,B)
proof
  let B be Subset of GX, p be Point of GX;
  assume
A1: p in B;
  then reconsider B9 = B as non empty Subset of GX;
  reconsider q=p as Point of GX|B9 by A1,PRE_TOPC:8;
  q in Component_of q by CONNSP_1:38;
  hence thesis by A1,Def7;
end;
