On the Coincidence of the Classes of Finite Groups $ E_{pi_{x}} $ and $ D_{pi_{x}} $

Let ( pi_{x} ) be the set of primes greater than ( x ). We prove that for all( xin{??} ) the classes of finite groups ( D_{pi_{x}} ) and ( E_{pi_{x}} )coincide; i.e., a finite group ( G ) possesses a ( pi_{x} )-Hall subgroup if and onlyif ( G ) satisfies the complete analog of the Sylow Theorems for a ( pi_{x} )-subgroup.