\imp\and右侧右拆分
theorem imp_and_splitrsl (A B C: wff): $ (A \imp B \and C) \imp A \imp B $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imp_tran | ((A \imp B \and C) \imp (A \imp B) \and (A \imp C)) \imp ((A \imp B) \and (A \imp C) \imp A \imp B) \imp (A \imp B \and C) \imp A \imp B |
|
| 2 | imp_and_insl | (A \imp B \and C) \imp (A \imp B) \and (A \imp C) |
|
| 3 | 1, 2 | ax_mp | ((A \imp B) \and (A \imp C) \imp A \imp B) \imp (A \imp B \and C) \imp A \imp B |
| 4 | and_splitl | (A \imp B) \and (A \imp C) \imp A \imp B |
|
| 5 | 3, 4 | ax_mp | (A \imp B \and C) \imp A \imp B |