In this context, $\phi$ and $\psi$ are formulas and $\Gamma$ is a set of formulas.
I'm not quite sure what it means. Does it mean $\Gamma \vdash (\phi \Rightarrow \psi)$ or does it mean $(\Gamma \vdash \phi )\Rightarrow \psi$ ?
The following is the exact context of my question. It is from the Handbook of Proof Theory by Samuel R. Buss on page 6 (page 16 if including the preface, table of contents etc.)
Also, if you could explain section (b) in more detail to me, that would be much appreciated as well. I don't think I really grasp it fully.