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

Replace $n$ with $3$ and you have a proof that $p\to p$ follows from no assumptions. Thence it will follow from any assumption at all, including an assumption of $p$. — Graham Kemp, Jul 06 '18 at 02:06
If you have a proof of something from no assumptions you can always weaken it to a proof with assumptions. Just assume some statements at the beginning and don’t do anything with them. — spaceisdarkgreen, Jul 06 '18 at 02:28
See he explanation in the answer to the post How is the implication introduction used here ? — Mauro ALLEGRANZA, Jul 06 '18 at 06:51

score 1 · Answer 1 · answered Feb 23 '19 at 05:23

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:

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

Fitch-style Deductive Proof

1 Answers1