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| Mirrors > Home > MPE Home > Th. List > imbitrid | Structured version Visualization version GIF version | ||
| Description: A mixed syllogism inference. (Contributed by NM, 12-Jan-1993.) |
| Ref | Expression |
|---|---|
| imbitrid.1 | ⊢ (𝜑 → 𝜓) |
| imbitrid.2 | ⊢ (𝜒 → (𝜓 ↔ 𝜃)) |
| Ref | Expression |
|---|---|
| imbitrid | ⊢ (𝜒 → (𝜑 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imbitrid.1 | . 2 ⊢ (𝜑 → 𝜓) | |
| 2 | imbitrid.2 | . . 3 ⊢ (𝜒 → (𝜓 ↔ 𝜃)) | |
| 3 | 2 | biimpd 229 | . 2 ⊢ (𝜒 → (𝜓 → 𝜃)) |
| 4 | 1, 3 | syl5 34 | 1 ⊢ (𝜒 → (𝜑 → 𝜃)) |
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