Proving the low energy theorem of hidden local symmetry

Based on the Ward-Takahashi identity for the Becchi-Rouet-Stora symmetry, we prove to all orders of the loop expansion the low energy theorem of hidden local symmetry for the vector mesons (a version of the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation) in the U(N${)}_{\mathit{L}}$×U(N${)}_{\mathit{R}}$/U(N${)}_{\mathit{V}}$ nonlinear chiral Lagrangian.