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
  (SAT M).(A '&' B) = 1 iff (SAT M).A = 1 & (SAT M).B = 1
  proof
    hereby
      assume (SAT M).(A '&' B) = 1;then
      (SAT M).A '&' (SAT M).B = 1 by semcon2;
      hence (SAT M).A = 1 & (SAT M).B = 1 by XBOOLEAN:101;
    end;
    assume A3:(SAT M).A = 1 & (SAT M).B = 1;
    thus (SAT M).(A '&' B) = (SAT M).A '&' (SAT M).B by semcon2
    .= 1 by A3;
  end;
