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 Th43: (p => (q '&&' ('not' q))) => ('not' p) is ctaut
  proof
   let g;
   set v = VAL g;
A1: v.tf = 0 by LTLAXIO1:def 15;
A2: v.p = 1 or v.p = 0 by XBOOLEAN:def 3;
A3: v.q = 1 or v.q = 0 by XBOOLEAN:def 3;
    thus v.((p => (q '&&' ('not' q))) => ('not' p))
    = v.(p => (q '&&' ('not' q))) => v.('not' p) by LTLAXIO1:def 15
    .= v.p => v.(q '&&' ('not' q)) => v.('not' p) by LTLAXIO1:def 15
    .= v.p => (v.q '&' v.('not' q)) => v.('not' p) by LTLAXIO1:31
    .= v.p => (v.q '&' (v.q => v.tf)) => v.('not' p) by LTLAXIO1:def 15
    .= 1 by A2,A3,A1,LTLAXIO1:def 15;
  end;
