theorem
  M,v |= (p => 'not' q) => (q => 'not' p) & M |= (p => 'not' q) => (q =>
  'not' p)
proof
  now
    let v;
    now
      assume M,v |= p => 'not' q;
      then M,v |= p implies M,v |= 'not' q by ZF_MODEL:18;
      then M,v |= q implies M,v |= 'not' p by ZF_MODEL:14;
      hence M,v |= q => 'not' p by ZF_MODEL:18;
    end;
    hence M,v |= (p => 'not' q) => (q => 'not' p) by ZF_MODEL:18;
  end;
  hence thesis;
end;
