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$P_n$ is $n$-$th$ prime number then $P_{n+m} \ge P_n+P_m$

Let $n$, $m$ are two positive integer numbers, $P_n$ is $n$-$th$ prime number. How I can prove that:

$$P_{n+m} \ge P_n+P_m$$

Can you give for me a hint, a reference, or a comment, or a proof?