Why Does the Shell Theorem Lemma Allow Multiplication by \cos \varphi?

[TMO]

I am concerned regarding a lemma of the shell theorem. Specifically, I am concerned with the idea that due to the vector nature of the forces, that one can simplify this:

into this:

Could somebody precisely explain why we're allowed to multiply in the \cos \varphi in the second equation?

 

[maverick_starstrider]

It's a dot product with the radius unit vector. You're projecting the contribution of dF (which I'm inferring is along s) along the radius vector r