reserve A,B,C,D,p,q,r for Element of LTLB_WFF,
        F,G,X for Subset of LTLB_WFF,
        M for LTLModel,
        i,j,n for Element of NAT,
        f,f1,f2,g for FinSequence of LTLB_WFF;

theorem th16:
  (A => B) => ((B => C) => (A => C)) is LTL_TAUT_OF_PL
  proof
    let g be Function of LTLB_WFF,BOOLEAN;
    set v = VAL g;
A1: v.A = 1 or v.A = 0 by XBOOLEAN:def 3;
A2: v.B = 1 or v.B = 0 by XBOOLEAN:def 3;
A3: v.C = 1 or v.C = 0 by XBOOLEAN:def 3;
    thus v.((A => B) => ((B => C) => (A => C)))
    = v.(A => B) => v.((B => C) => (A => C)) by LTLAXIO1:def 15
    .= v.A => v.B => v.((B => C) => (A => C)) by LTLAXIO1:def 15
    .= v.A => v.B => (v.(B => C) => v.(A => C)) by LTLAXIO1:def 15
    .= v.A => v.B => ((v.B => v.C) => v.(A => C)) by LTLAXIO1:def 15
    .= 1 by A1,A2,A3,LTLAXIO1:def 15;
 end;
