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 '&' q) => q is tautology
  proof
    let M;
    thus (SAT M).((p '&' q) => q) = (SAT M).(p '&' q) => (SAT M).q by Def11
    .= ((SAT M).p '&' (SAT M).q) => (SAT M).q by semcon2
    .= 1 by th1;
  end;
