The strong multiplicity one in automorphic representation theory says that if two
automorphic cuspidal irreducible representations on $\text{GL}_n$ have isomorphic
local components for all but a finite number of places, then they are isomorphic. As
the analog of this, the strong multiplicity one for the Selberg class conjectures
that for functions $F$ and $G$ with $F(s) = \sum_{n=1}^\infty a_F(n)n^{-s}$ and
$G(s) = \sum_{n=1}^\infty a_G(n)n^{-s}$ in this class, if $a_F(p)=a_G(p)$ for all
but finitely many primes $p$, then $F=G$. In this article, we prove this
conjecture.