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| Mirrors > Home > MPE Home > Th. List > impancom | Structured version Visualization version GIF version | ||
| Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013.) |
| Ref | Expression |
|---|---|
| impancom.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
| Ref | Expression |
|---|---|
| impancom | ⊢ ((𝜑 ∧ 𝜒) → (𝜓 → 𝜃)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | impancom.1 | . . . 4 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) | |
| 2 | 1 | ex 412 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
| 3 | 2 | com23 86 | . 2 ⊢ (𝜑 → (𝜒 → (𝜓 → 𝜃))) |
| 4 | 3 | imp 406 | 1 ⊢ ((𝜑 ∧ 𝜒) → (𝜓 → 𝜃)) |
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