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| Mirrors > Home > MPE Home > Th. List > sylbird | Structured version Visualization version GIF version | ||
| Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994.) |
| Ref | Expression |
|---|---|
| sylbird.1 | ⊢ (𝜑 → (𝜒 ↔ 𝜓)) |
| sylbird.2 | ⊢ (𝜑 → (𝜒 → 𝜃)) |
| Ref | Expression |
|---|---|
| sylbird | ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sylbird.1 | . . 3 ⊢ (𝜑 → (𝜒 ↔ 𝜓)) | |
| 2 | 1 | biimprd 248 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 3 | sylbird.2 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) | |
| 4 | 2, 3 | syld 47 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
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