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 Th13:
  for A,B being Subset of GX st A is connected & B is connected &
  A<>{} & A c= B holds B c= Component_of A
proof
  let A,B be Subset of GX;
  assume that
A1: A is connected and
A2: B is connected and
A3: A<>{} & A c= B;
  Component_of A = Component_of B by A1,A2,A3,Th12;
  hence thesis by A2,Th1;
end;
