\neg消除右引入\imp
theorem neg_elimintror_imp (A B: wff): $ \neg A \imp A \imp B $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imp_imp_insl | (\neg A \imp (\neg B \imp \neg A) \imp A \imp B) \imp (\neg A \imp \neg B \imp \neg A) \imp \neg A \imp A \imp B |
|
| 2 | introl_imp | ((\neg B \imp \neg A) \imp A \imp B) \imp \neg A \imp (\neg B \imp \neg A) \imp A \imp B |
|
| 3 | neg_imp_elimrev | (\neg B \imp \neg A) \imp A \imp B |
|
| 4 | 2, 3 | ax_mp | \neg A \imp (\neg B \imp \neg A) \imp A \imp B |
| 5 | 1, 4 | ax_mp | (\neg A \imp \neg B \imp \neg A) \imp \neg A \imp A \imp B |
| 6 | introl_imp | \neg A \imp \neg B \imp \neg A |
|
| 7 | 5, 6 | ax_mp | \neg A \imp A \imp B |