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;

theorem Th6: p in tau1.p
  proof
    defpred P1[Element of l] means $1 in tau1.$1;
A1: for n holds P1[ prop n]
    proof
      let n;
      tau1.(prop n) = {prop n} by Def4;
      hence thesis by TARSKI:def 1;
    end;
A2: for r, s st P1[r] & P1[s] holds P1[r 'U' s] & P1[r => s]
    proof
      let r,s;
      assume that P1[r] and P1[s];
      tau1.(r 'U' s) = {r 'U' s} by Def4;
      hence P1[r 'U' s] by TARSKI:def 1;
      tau1.(r => s) = {r => s} \/ tau1.r \/ tau1.s by Def4;then
      {r => s} c= {r => s} \/ tau1.r & {r => s} \/ tau1.r c= tau1.(r => s)
      by XBOOLE_1:7;
      hence P1[r => s] by ZFMISC_1:31;
    end;
    tau1.TFALSUM = {TFALSUM} by Def4;
    then A3: P1[TFALSUM] by TARSKI:def 1;
    for p holds P1[p] from HILBERT2:sch 2(A3,A1,A2);
    hence thesis;
  end;
