# How do I apply the reduction to absurdity rule in the Open Logic natural deduction tool?

I'm using the open logic natural deduction tool (https://proofs.openlogicproject.org/) as it makes writing proofs very clear and clean but I can't seem to apply the reduction to absurdity rule correctly.

``````Construct a proof for the argument: ¬Q, R → P ∴ (P → Q) → ¬R

1   ¬Q
2   R → P
3       P → Q
4           R
5           P           →E 2, 4
6           Q           →E 3, 5
7           ¬Q          R 1
8           Q ∧ ¬Q      ∧I 6, 7
9       ¬R              ¬I 4–8
``````

I think I'm using the rule as stated in the corresponding section of the tool but I get an error message saying "Line 9: Is not a proper application of the rule ¬I (for the line(s) cited)." What am I doing wrong?

• Your line 8 can be simply changed to ⊥ (¬E 6, 7), line 9 then changed to ¬R (¬I 4–8), then in line 10 you can arrive at your conclusion (P → Q) → ¬R (→I 3–9) which can be verified quickly in your referenced open logic online tool... Feb 4, 2022 at 3:14
• Thanks! It worked :) Feb 4, 2022 at 3:22
• Now we must listen. Mar 4, 2023 at 14:37