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| Mirrors > Home > MPE Home > Th. List > mp3an23 | Structured version Visualization version GIF version | ||
| Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005.) |
| Ref | Expression |
|---|---|
| mp3an23.1 | ⊢ 𝜓 |
| mp3an23.2 | ⊢ 𝜒 |
| mp3an23.3 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| mp3an23 | ⊢ (𝜑 → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mp3an23.1 | . 2 ⊢ 𝜓 | |
| 2 | mp3an23.2 | . . 3 ⊢ 𝜒 | |
| 3 | mp3an23.3 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
| 4 | 2, 3 | mp3an3 1452 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
| 5 | 1, 4 | mpan2 691 | 1 ⊢ (𝜑 → 𝜃) |
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