I was assigned a problem to do for class and i don't understand how to do it. The proof is P ↔ Q Prove: (R ↔ P) ↔ (R ↔ Q) and I am using the book language logic and Proof.
Since you say that you don't understand how to start, I will give you a hint on the skeleton and leave the details for you to fill in:
Given that the main connective in your conclusion formula is ↔, you can be relatively sure that the last rule application is a ↔I, and according to the definition of the ↔I rule (read and apply the rule definitions!), you know that the skeleton of your proof must look like this:
You need two subproofs, one where you derive R↔Q from R↔P, and one where you derive R↔P from R↔Q.
Since the conclusions of these subproofs are again biconditionals, the "..."'s will have the same structure - in the first subproof with R↔Q as the conclusion, derive Q from R and R from Q; the second subproof (which I leave here with ...'s) works analogously:
In the "..." parts of the innermost subproofs, to get from R to Q and from Q to R etc., you will need to use the premise in line 1 and the premises in line 2 or 10, respectively, together with ↔E.
With this, I'm sure you will be able to figure out the rest on your own.