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 naa:
  F |- ('not' A => A) => A
  proof
    'not' A => 'not' A => (('not' A => A)=>A) in PL_axioms by withplax;then
A1: F |- ('not' A => 'not' A) => (('not' A => A)=>A) by th42;
    F |- 'not' A => 'not' A by thaa;
    hence thesis by A1,th43;
  end;
