Span(S) is the intersection of all subspaces of V containing S

[JD_PM]

Homework Statement:: I want to understand the proof for the following theorem: span(S) is the intersection of all subspaces of V containing S.
Relevant Equations:: N/A

I know that if $W$ is any subspace of $V$ containing $S$ then $\text{span}(S) \subseteq W$.

I have read (Page 157: # 4.86) that it follows that $S$ is contained in the intersection of all subspaces containing $S$ but I do not quite get why.

Once I understand the above I should be ready to move forward

Thanks!

 

[Office_Shredder]

This is just a general statement about sets. If $V\subset W_i$ for any collection of sets $W_i$ (the index here doesn't have to be the natural numbers, it can be uncountable), then
$$V\subset \bigcap_i W_i.$$