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| Mirrors > Home > MPE Home > Th. List > mpan2 | Structured version Visualization version GIF version | ||
| Description: An inference based on modus ponens. (Contributed by NM, 16-Sep-1993.) (Proof shortened by Wolf Lammen, 19-Nov-2012.) |
| Ref | Expression |
|---|---|
| mpan2.1 | ⊢ 𝜓 |
| mpan2.2 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Ref | Expression |
|---|---|
| mpan2 | ⊢ (𝜑 → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpan2.1 | . . 3 ⊢ 𝜓 | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → 𝜓) |
| 3 | mpan2.2 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 4 | 2, 3 | mpdan 687 | 1 ⊢ (𝜑 → 𝜒) |
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