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| Mirrors > Home > MPE Home > Th. List > mpsyl | Structured version Visualization version GIF version | ||
| Description: Modus ponens combined with a syllogism inference. (Contributed by Alan Sare, 20-Apr-2011.) |
| Ref | Expression |
|---|---|
| mpsyl.1 | ⊢ 𝜑 |
| mpsyl.2 | ⊢ (𝜓 → 𝜒) |
| mpsyl.3 | ⊢ (𝜑 → (𝜒 → 𝜃)) |
| Ref | Expression |
|---|---|
| mpsyl | ⊢ (𝜓 → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpsyl.1 | . . 3 ⊢ 𝜑 | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝜓 → 𝜑) |
| 3 | mpsyl.2 | . 2 ⊢ (𝜓 → 𝜒) | |
| 4 | mpsyl.3 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) | |
| 5 | 2, 3, 4 | sylc 65 | 1 ⊢ (𝜓 → 𝜃) |
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