theorem
  M,v |= 'not' p 'or' 'not' q => 'not'(p '&' q) & M |= 'not' p 'or'
  'not' q => 'not'(p '&' q)
proof
  now
    let v;
    now
      assume M,v |= 'not' p 'or' 'not' q;
      then M,v |= 'not' p or M,v |= 'not' q by ZF_MODEL:17;
      then not M,v |= p or not M,v |= q by ZF_MODEL:14;
      then not M,v |= p '&' q by ZF_MODEL:15;
      hence M,v |= 'not'(p '&' q) by ZF_MODEL:14;
    end;
    hence M,v |= 'not' p 'or' 'not' q => 'not'(p '&' q) by ZF_MODEL:18;
  end;
  hence thesis;
end;
