| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > sylbid | Structured version Visualization version GIF version | ||
| Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994.) |
| Ref | Expression |
|---|---|
| sylbid.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| sylbid.2 | ⊢ (𝜑 → (𝜒 → 𝜃)) |
| Ref | Expression |
|---|---|
| sylbid | ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sylbid.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 2 | 1 | biimpd 229 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 3 | sylbid.2 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) | |
| 4 | 2, 3 | syld 47 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Copyright terms: Public domain | W3C validator |