| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > mpan2d | Structured version Visualization version GIF version | ||
| Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004.) |
| Ref | Expression |
|---|---|
| mpan2d.1 | ⊢ (𝜑 → 𝜒) |
| mpan2d.2 | ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) |
| Ref | Expression |
|---|---|
| mpan2d | ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpan2d.1 | . 2 ⊢ (𝜑 → 𝜒) | |
| 2 | mpan2d.2 | . . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃)) | |
| 3 | 2 | expd 415 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| 4 | 1, 3 | mpid 44 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Copyright terms: Public domain | W3C validator |