reserve A,B,p,q,r,s for Element of LTLB_WFF,
  n for Element of NAT,
  X for Subset of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN,
  x,y for set;
reserve P,Q,P1,R for PNPair;

theorem for P be consistent PNPair holds not TFALSUM in rng P`1
  proof
    let P be consistent PNPair;
    assume TFALSUM in rng P`1;
    then {}l |- 'not' (P^) by Th28;
    hence contradiction by Def10;
  end;
