On the characterization of the core of a $\pi$-prefrattini subgroup of a finite soluble group

Let $\pi$ be a set of primes and let $H$ be a $\pi$-prefrattini subgroup of a finite soluble group $G$. We prove that there exist elements $x, y, z\in G$ such that $H\cap H^x\cap H^y\cap H^z=\Phi_\pi(G)$.