reserve a,b,c for boolean object;
reserve p,q,r,s,A,B,C for Element of LTLB_WFF,
        F,G,X,Y for Subset of LTLB_WFF,
        i,j,k,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;
reserve M for LTLModel;

theorem Th35:
 (p=>(q=>r))=>((p=>q)=>(p=>r)) in LTL_axioms
 proof
  (p=>(q=>r))=>((p=>q)=>(p=>r)) is LTL_TAUT_OF_PL
  proof
   let f be Function of LTLB_WFF,BOOLEAN;
   A1: (VAL f).p=0 or(VAL f).p=1 by XBOOLEAN:def 3;
   A2: (VAL f).q=0 or(VAL f).q=1 by XBOOLEAN:def 3;
   A3: (VAL f).r=0 or(VAL f).r=1 by XBOOLEAN:def 3;
   thus(VAL f).((p=>(q=>r))=>((p=>q)=>(p=>r)))=(VAL f).(p=>(q=>r))=>(VAL f).((p
=>q)=>(p=>r)) by Def15
    .=((VAL f).p=>(VAL f).(q=>r))=>(VAL f).((p=>q)=>(p=>r)) by Def15
    .=((VAL f).p=>((VAL f).q=>(VAL f).r))=>(VAL f).((p=>q)=>(p=>r)) by Def15
    .=((VAL f).p=>((VAL f).q=>(VAL f).r))=>((VAL f).(p=>q)=>(VAL f).(p=>r)) by
Def15
    .=((VAL f).p=>((VAL f).q=>(VAL f).r))=>(((VAL f).p=>(VAL f).q)=>(VAL f).(p
=>r)) by Def15
    .=1 by A1,A2,A3,Def15;
  end;
  hence (p=>(q=>r))=>((p=>q)=>(p=>r)) in LTL_axioms by Def17;
 end;
