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| Mirrors > Home > MPE Home > Th. List > sylc | Structured version Visualization version GIF version | ||
| Description: A syllogism inference combined with contraction. (Contributed by NM, 4-May-1994.) (Revised by NM, 13-Jul-2013.) |
| Ref | Expression |
|---|---|
| sylc.1 | ⊢ (𝜑 → 𝜓) |
| sylc.2 | ⊢ (𝜑 → 𝜒) |
| sylc.3 | ⊢ (𝜓 → (𝜒 → 𝜃)) |
| Ref | Expression |
|---|---|
| sylc | ⊢ (𝜑 → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sylc.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | sylc.2 | . . 3 ⊢ (𝜑 → 𝜒) | |
| 3 | sylc.3 | . . 3 ⊢ (𝜓 → (𝜒 → 𝜃)) | |
| 4 | 1, 2, 3 | syl2im 40 | . 2 ⊢ (𝜑 → (𝜑 → 𝜃)) |
| 5 | 4 | pm2.43i 52 | 1 ⊢ (𝜑 → 𝜃) |
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