I know how to use the Conditional Premises rule, but I'm not sure how it works when to apply it. For example:

Using sentential calculus (with a four column format), prove s ⇒ r follows from the premises p ⇒ (q ⇒ r), p ∨ ~s, and q.

The proof looks like this:

Code:

{Pr1} 1. p ⇒ (q ⇒ r) P
{Pr2} 2. p ∨ ~s P
{Pr3} 3. q P
{Pr4} 4. s P (for CP)
{Pr2, Pr4} 5. p DS (2, 4)
{Pr1, Pr2, Pr4} 6. q ⇒ r MP (1, 5)
{Pr1, Pr2, Pr3, Pr4} 7. r MP (3, 6)
{Pr1, Pr2, Pr3} 8. s ⇒ r C (4, 7)

How do I know *when* to use Conditional Premises? Is it only after I've exhausted all other methods? Also, could you explain to me briefly why one is allowed to say that a statement true, if its truth is based on something that you simply defined earlier? It just doesn't make sense to me at this point.