\imp\or左分配
theorem imp_or_distl (A B C: wff): $ A \imp B \or C \iff (A \imp B) \or (A \imp C) $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iff_comp | ((A \imp B \or C) \imp (A \imp B) \or (A \imp C)) \imp ((A \imp B) \or (A \imp C) \imp A \imp B \or C) \imp (A \imp B \or C \iff (A \imp B) \or (A \imp C)) |
|
| 2 | imp_or_insl | (A \imp B \or C) \imp (A \imp B) \or (A \imp C) |
|
| 3 | 1, 2 | ax_mp | ((A \imp B) \or (A \imp C) \imp A \imp B \or C) \imp (A \imp B \or C \iff (A \imp B) \or (A \imp C)) |
| 4 | imp_or_extl | (A \imp B) \or (A \imp C) \imp A \imp B \or C |
|
| 5 | 3, 4 | ax_mp | A \imp B \or C \iff (A \imp B) \or (A \imp C) |