Fitch-style Deductive Proof

Question

I am having trouble with the following question:

Give natural deduction proofs of the following formulas (from no assumptions): $p \to p$.

Here is what I have so far:

$$\begin{array}{|l}\hline~~\begin{array}{|l}1.~p \\\hline 2.~p \end{array}&\raise {1ex}{\rm A\\\rm R,1} \\n.~ p\to p &\rm I\to,1{-}2\end{array}$$

How do I proceed if I want to prove that $p\to p$ follows from the assumption $p$? I know that this question is poorly formatted, but any help would still be appreciated.

Thanks

Answer 1

Yes, your proof is correct. Here are the steps you provided in a proof checker showing they are correct:

This proof checker would accept even a shorter proof:

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Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/