On a Special Case of Dirichlet's Theorem

Let $p$ be a prime number, and $h$ a positive integer such that $\gcd (p,h)=1$. We prove, without invoking Dirichlet’s theorem, that the arithmetic progression $p(\mathbf{N}\cup \{0\})+h$ contains infinitely many prime numbers. This is a special case of Dirichlet’s theorem not considered by other authors.