  Recently a perturbative theory has been constructed, starting from the
Feynman rules of the nonlinear sigma model at the tree level in the presence of
an external vector source coupled to the flat connection and of a scalar source
coupled to the nonlinear sigma model constraint (flat connection formalism).
  The construction is based on a local functional equation, which overcomes the
problems due to the presence (already at one loop) of non chiral symmetric
divergences. The subtraction procedure of the divergences in the loop expansion
is performed by means of minimal subtraction of properly normalized amplitudes
in dimensional regularization.
  In this paper we complete the study of this subtraction procedure by giving
the formal proof that it is symmetric to all orders in the loopwise expansion.
  We provide further arguments on the issue that, within our subtraction
strategy, only two parameters can be consistently used as physical constants.
