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| Mirrors > Home > MPE Home > Th. List > mpisyl | Structured version Visualization version GIF version | ||
| Description: A syllogism combined with a modus ponens inference. (Contributed by Alan Sare, 25-Jul-2011.) |
| Ref | Expression |
|---|---|
| mpisyl.1 | ⊢ (𝜑 → 𝜓) |
| mpisyl.2 | ⊢ 𝜒 |
| mpisyl.3 | ⊢ (𝜓 → (𝜒 → 𝜃)) |
| Ref | Expression |
|---|---|
| mpisyl | ⊢ (𝜑 → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpisyl.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | mpisyl.2 | . . 3 ⊢ 𝜒 | |
| 3 | mpisyl.3 | . . 3 ⊢ (𝜓 → (𝜒 → 𝜃)) | |
| 4 | 2, 3 | mpi 20 | . 2 ⊢ (𝜓 → 𝜃) |
| 5 | 1, 4 | syl 17 | 1 ⊢ (𝜑 → 𝜃) |
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