
theorem Th5:
  for GX being TopStruct, A, B being Subset of GX holds A
  is_a_component_of B implies A c= B
proof
  let GX be TopStruct, A, B be Subset of GX;
  assume A is_a_component_of B;
  then
A1: ex B1 being Subset of GX|B st B1 = A & B1 is a_component by CONNSP_1:def 6;
  the carrier of GX|B = B by PRE_TOPC:8;
  hence thesis by A1;
end;
