reserve A,B,p,q,r,s for Element of LTLB_WFF,
  i,j,k,n for Element of NAT,
  X for Subset of LTLB_WFF,
  f,f1 for FinSequence of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN;

theorem X |- p => (q '&&' ('not' q)) implies X |- 'not' p
  proof
    (p => (q '&&' ('not' q))) => ('not' p) is ctaut by Th43;then
    (p => (q '&&' ('not' q))) => ('not' p) in LTL_axioms by LTLAXIO1:def 17;
    then A1: X |- (p => (q '&&' ('not' q))) => ('not' p) by LTLAXIO1:42;
    assume X |- p => (q '&&' ('not' q));
    hence X |- 'not' p by A1,LTLAXIO1:43;
  end;
