Q:

question about the forms of prime numbers

I was thinking about primes earlier and I thought of a hypothesis that I have been unable to prove.  I was wondering whether it was a known theorem and whether anyone knows a proof or can prove (or disprove) it. 
here it is:
there are an infinite number of primes that satisfy the equation:
$p \equiv a \bmod n$
for all A and N where A and N are relatively prime. 

A:

This is Dirichlet's theorem on arithmetic progressions of primes.  A brief sketch of the proof is given in the article, along with a reference to Jürgen Neukirch's Algebraic number theory $(1999)$.

