On $\sigma$-subnormal subgroups of finite groups

Let $p$ be a prime and let $\sigma = \{\{p\}, \{p\}'\}$ be a partition of the set ${\Bbb P}$ of all primes. We prove the following conjecture by Skiba: If each complete Hall set of type $\sigma$ in a finite group $G$ is reducible to some subgroup $H$ of $G$ then $H$ is $\sigma$-subnormal in $G$.