How do I show this?

Theorem 4.20. Every regular space is hereditarily regular. Definition. Let P be a topological property (such as 71, Hausdorff, etc.). A topological space X is hereditarily P if and only if for each subspace Y of X, the space Y has property P when Y is given the relative topology from X. X is regular if and only if for every point x E X and closed set A C X not containing x, there are disjoint open sets U, V such that x E U and A C V. A T3-space is any space that is both T, and regular