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| Mirrors > Home > MPE Home > Th. List > syld3an3 | Structured version Visualization version GIF version | ||
| Description: A syllogism inference. (Contributed by NM, 20-May-2007.) |
| Ref | Expression |
|---|---|
| syld3an3.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
| syld3an3.2 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) |
| Ref | Expression |
|---|---|
| syld3an3 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simp1 1137 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑) | |
| 2 | simp2 1138 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜓) | |
| 3 | syld3an3.1 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
| 4 | syld3an3.2 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) | |
| 5 | 1, 2, 3, 4 | syl3anc 1373 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜏) |
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