Perfectly normal implies hereditarily normal

Statement
Any perfectly normal space is a hereditarily normal space -- every subspace of it is a normal space.

Related facts

 * Metrizable implies hereditarily normal
 * Monotonically normal implies hereditarily normal

Facts used

 * 1) uses::Perfect normality is hereditary
 * 2) uses::Perfectly normal implies normal

Proof
By fact (1), every subspace of a perfectly normal space is perfectly normal, and by fact (2), every subspace is normal.