Subsequence of Subsequence

Theorem
Let $s$ be a set.

Let $\sequence {s_n}$ be a sequence in $S$.

Let $\sequence {s_m}$ be a subsequence of $\sequence {s_n}$.

Let $\sequence {s_k}$ be a subsequence of $\sequence {s_m}$.

Then $\sequence {s_k}$ is a subsequence of $\sequence {s_n}$.