  Basing on some new and concise forms of the Callan-Symanzik equations, the
low-energy theorems involving trace anomalies \`a la
Novikov-Shifman-Vainshtein-Zakharov, first advanced and proved in Nucl. Phys.
\textbf{B165}, 67 (1980), \textbf{B191}, 301 (1981), are proved as immediate
consequences. The proof is valid in any consistent effective field theories and
these low-energy theorems are hence generalized. Some brief discussions about
related topics are given.
