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| Mirrors > Home > MPE Home > Th. List > sylanb | Structured version Visualization version GIF version | ||
| Description: A syllogism inference. (Contributed by NM, 18-May-1994.) |
| Ref | Expression |
|---|---|
| sylanb.1 | ⊢ (𝜑 ↔ 𝜓) |
| sylanb.2 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
| Ref | Expression |
|---|---|
| sylanb | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sylanb.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | 1 | biimpi 216 | . 2 ⊢ (𝜑 → 𝜓) |
| 3 | sylanb.2 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
| 4 | 2, 3 | sylan 580 | 1 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
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