reserve p,q,r,s,A,B for Element of PL-WFF,
  F,G,H for Subset of PL-WFF,
  k,n for Element of NAT,
  f,f1,f2 for FinSequence of PL-WFF;
reserve M for PLModel;

theorem
  p => r => (q => r => ((p 'or' q) => r)) is tautology
  proof
    let M;
A3: (SAT M).(q => r => ((p 'or' q) => r))
    = (SAT M).(q => r) => (SAT M).((p 'or' q) => r) by Def11
    .= (SAT M).q => (SAT M).r => (SAT M).((p 'or' q) => r) by Def11
    .= (SAT M).q => (SAT M).r => ((SAT M).(p 'or' q) => (SAT M).r) by Def11
    .= (SAT M).q => (SAT M).r => (((SAT M).p 'or' (SAT M).q) => (SAT M).r)
    by semdis2;
    thus (SAT M).(p => r => (q => r => ((p 'or' q) => r)))
    = (SAT M).(p => r) => (SAT M).(q => r => ((p 'or' q) => r)) by Def11
    .= (SAT M).p => (SAT M).r => ((SAT M).q => (SAT M).r
    => (((SAT M).p 'or' (SAT M).q) => (SAT M).r)) by Def11,A3
    .= 1 by th5a;
  end;
