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| Mirrors > Home > MPE Home > Th. List > biimtrdi | Structured version Visualization version GIF version | ||
| Description: A mixed syllogism inference. (Contributed by NM, 2-Jan-1994.) |
| Ref | Expression |
|---|---|
| biimtrdi.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
| biimtrdi.2 | ⊢ (𝜒 → 𝜃) |
| Ref | Expression |
|---|---|
| biimtrdi | ⊢ (𝜑 → (𝜓 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biimtrdi.1 | . . 3 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
| 2 | 1 | biimpd 229 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 3 | biimtrdi.2 | . 2 ⊢ (𝜒 → 𝜃) | |
| 4 | 2, 3 | syl6 35 | 1 ⊢ (𝜑 → (𝜓 → 𝜃)) |
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