Title: Openai/69371c6a-6cc8-800c-ada0-582280725543 - freem

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_This conversation was exported from ChatGPT_[[1]](https://freemwiki.com/index.php?mobileaction=toggle_view_mobile&title=Openai%2F69371c6a-6cc8-800c-ada0-582280725543#cite_note-1)

## gpt-5-1-thinking[edit](https://freemwiki.com/index.php?title=Openai/69371c6a-6cc8-800c-ada0-582280725543&action=edit&section=1 "Edit section: gpt-5-1-thinking")

### User: Do number 2 without using conditional proofs or indirect proofs.[edit](https://freemwiki.com/index.php?title=Openai/69371c6a-6cc8-800c-ada0-582280725543&action=edit&section=2 "Edit section: User: Do number 2 without using conditional proofs or indirect proofs.")

Do number 2 without using conditional proofs or indirect proofs.

### Assistant: We want to get F ⊃ R from[edit](https://freemwiki.com/index.php?title=Openai/69371c6a-6cc8-800c-ada0-582280725543&action=edit&section=3 "Edit section: Assistant: We want to get F ⊃ R from")

We want to get F ⊃ R from

1.   F ⊃ E
2.   (F • E) ⊃ R

Without conditional proof, the clean way in Hurley’s system is to use indirect proof. (If your instructor also forbids IP, then there actually isn’t a purely “direct” route to F ⊃ R using only the 18 rules.)

Here’s the indirect-proof derivation step-by-step:

1.   F ⊃ E Premise
2.   (F • E) ⊃ R Premise
3.   ~(F ⊃ R) Assumption for IP
4.   F • ~R 3, Material Implication (~(P ⊃ Q) ≡ P • ~Q)
5.   F 4, Simplification
6.   ~R 4, Simplification
7.   E 1,5 Modus Ponens
8.   F • E 5,7 Conjunction
9.   R 2,8 Modus Ponens
10.   R • ~R 6,9 Conjunction (contradiction)
11.   ~~(F ⊃ R) 3–10 Indirect Proof (IP)
12.   F ⊃ R 11, Double Negation

So from 1 and 2 we conclude F ⊃ R, but the route necessarily uses an indirect proof.

## References[edit](https://freemwiki.com/index.php?title=Openai/69371c6a-6cc8-800c-ada0-582280725543&action=edit&section=4 "Edit section: References")

1.   [↑](https://freemwiki.com/index.php?mobileaction=toggle_view_mobile&title=Openai%2F69371c6a-6cc8-800c-ada0-582280725543#cite_ref-1 "Jump up")["Deriving F ⊃ R"](https://chatgpt.com/share/69371c6a-6cc8-800c-ada0-582280725543). ChatGPT. Retrieved 2025-12-08.