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;
reserve x,y for set;

theorem inder:
  F is maximal & F is consistent implies  for p holds F |- p iff p in F
  proof
    assume A1: F is maximal & F is consistent;
    let p;
    hereby
      assume A2: F |- p;
      assume not p in F;then
      'not' p in F by A1;then
      F |- 'not' p by th42;
      hence contradiction by A2,A1;
    end;
    assume p in F;
    hence F |- p by th42;
  end;
