theorem Th5:
  X is closed_wrt_A1-A7 & A in X & B in X implies A/\B in X
proof
  assume that
A1: X is closed_wrt_A1-A7 & A in X and
A2: B in X;
  A\B in X by A1,A2,Th4;
  then A\(A\B) in X by A1,Th4;
  hence thesis by XBOOLE_1:48;
end;
