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 'or' q) <=> (q 'or' p) is tautology
  proof
    let M;
    thus (SAT M).((p 'or' q) <=> (q 'or' p)) =
    (SAT M).(p 'or' q) <=> (SAT M).(q 'or' p) by semequ2
    .= ((SAT M).p 'or' (SAT M).q) <=> (SAT M).(q 'or' p) by semdis2
    .= ((SAT M).p 'or' (SAT M).q) <=> ((SAT M).q 'or' (SAT M).p) by semdis2
    .= 1 by th6a;
  end;
