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 semequ2:
  (SAT M).(A <=> B) = (SAT M).A <=> (SAT M).B
  proof
    thus (SAT M).(A <=> B) = (SAT M).(A => B) '&' (SAT M).(B => A) by semcon2
    .= ((SAT M).A => (SAT M).B) '&' (SAT M).(B => A) by Def11
    .= (SAT M).A <=> (SAT M).B by Def11;
    end;
