First of all, please don't close this question cause I don't get the explanation given in: Use the Fitch system to prove the tautology (p ∨ ¬p)

I have been trying to solve this exercise for days now. I'm stuck in step 9: enter image description here

Any thoughts? Thank you.

  • Why do you think that is not a duplicate ? In the linked post there is a Fitch proof: instead of retrying with a new post, why not checking it ? Apr 20, 2020 at 15:13
  • You step 4 is the wrong one: use the contradiction with 1 and 3 to derive not-p. Apr 20, 2020 at 15:14
  • The explanation Virmaior gives is very unclear and it is 3 years old. I haven't been able to solve it based on his explanation. That's why I need a new input.
    – Luen
    Apr 20, 2020 at 15:15
  • 1
    Having derived not-p, you discharge 1 to get : not-(p or not-p) to not-p. Having done so, repeat all the derivation from 1 with the new assumption not-p in 2. In this case you get not-(not-p) and discharge again the assumption to get: not-(p or not-p) to not-(not-p). Now you can apply negation-intro rule (as above) to conclude with not-( not-(p or not-p) ). Apr 20, 2020 at 16:08
  • 1
    Step 12 is same as 3 and 4 will be not-p to (p or not-p). And so on. Apr 20, 2020 at 16:31

1 Answer 1


In step 10, you need to assume ~(p | ~p) again, in order to use Negation Introduction.

In full:

enter image description here

  • Nevermind, I just fixed it and was able to solve it. MANY THANKS F. Zer! You saved my life today
    – Luen
    Apr 20, 2020 at 17:39
  • You are welcome, @Nagma. Glad it helped.
    – F. Zer
    Apr 20, 2020 at 18:09

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