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