Pronormality is normalizer-closed

Statement
If $$H$$ is a pronormal subgroup of a group $$G$$, so is the normalizer $$N_G(H)$$.

Facts used

 * 1) uses::Normalizer of pronormal implies abnormal
 * 2) uses::Abnormal implies pronormal

Proof
The proof follows by piecing together facts (1) and (2).