\imp左同化
theorem imp_imp_assiml (A B: wff): $ (A \imp A \imp B) \imp A \imp B $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imp_imp_insl | (A \imp (A \imp B) \imp B) \imp (A \imp A \imp B) \imp A \imp B |
|
| 2 | imp_imp_swapl | ((A \imp B) \imp A \imp B) \imp A \imp (A \imp B) \imp B |
|
| 3 | imp_refl | (A \imp B) \imp A \imp B |
|
| 4 | 2, 3 | ax_mp | A \imp (A \imp B) \imp B |
| 5 | 1, 4 | ax_mp | (A \imp A \imp B) \imp A \imp B |