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| Mirrors > Home > MPE Home > Th. List > 3syl | Structured version Visualization version GIF version | ||
| Description: Inference chaining two syllogisms syl 17. Inference associated with imim12i 62. (Contributed by NM, 28-Dec-1992.) |
| Ref | Expression |
|---|---|
| 3syl.1 | ⊢ (𝜑 → 𝜓) |
| 3syl.2 | ⊢ (𝜓 → 𝜒) |
| 3syl.3 | ⊢ (𝜒 → 𝜃) |
| Ref | Expression |
|---|---|
| 3syl | ⊢ (𝜑 → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3syl.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
| 2 | 3syl.2 | . . 3 ⊢ (𝜓 → 𝜒) | |
| 3 | 1, 2 | syl 17 | . 2 ⊢ (𝜑 → 𝜒) |
| 4 | 3syl.3 | . 2 ⊢ (𝜒 → 𝜃) | |
| 5 | 3, 4 | syl 17 | 1 ⊢ (𝜑 → 𝜃) |
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