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| Mirrors > Home > MPE Home > Th. List > mpid | Structured version Visualization version GIF version | ||
| Description: A nested modus ponens deduction. Deduction associated with mpi 20. (Contributed by NM, 14-Dec-2004.) |
| Ref | Expression |
|---|---|
| mpid.1 | ⊢ (𝜑 → 𝜒) |
| mpid.2 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| Ref | Expression |
|---|---|
| mpid | ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpid.1 | . . 3 ⊢ (𝜑 → 𝜒) | |
| 2 | 1 | a1d 25 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 3 | mpid.2 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
| 4 | 2, 3 | mpdd 43 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
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