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 Th49: p => r => (q => r => ((p 'or' q) => r)) is ctaut
  proof
    let g;
    set v = VAL g;
A1: v.p = 1 or v.p = 0 by XBOOLEAN:def 3;
A2: v.r = 1 or v.r = 0 by XBOOLEAN:def 3;
A3: v.(p => r) = v.p => v.r by LTLAXIO1:def 15;
A4: v.q = 1 or v.q = 0 by XBOOLEAN:def 3;
    v.(q => r => ((p 'or' q) => r))
    = v.(q => r) => v.((p 'or' q) => r) by LTLAXIO1:def 15
    .= v.q => v.r => v.((p 'or' q) => r) by LTLAXIO1:def 15
    .= v.q => v.r => (v.(p 'or' q) => v.r) by LTLAXIO1:def 15
    .= v.q => v.r => ((v.p 'or' v.q) => v.r) by Th5;
    hence v.(p => r => (q => r => ((p 'or' q) => r)))
    = v.p => v.r => (v.q => v.r => ((v.p 'or' v.q) => v.r))
    by LTLAXIO1:def 15,A3
    .= 1 by A1,A2,A4;
  end;
