theorem
  proj2_3(X /\ Y) c= proj2_3 X /\ proj2_3 Y
proof
  proj2_3(X /\ Y) c= proj2_3 X & proj2_3(X /\ Y) c= proj2_3 Y
   by Th11,XBOOLE_1:17;
 hence thesis by XBOOLE_1:19;
end;
