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| Mirrors > Home > MPE Home > Th. List > impcom | Structured version Visualization version GIF version | ||
| Description: Importation inference with commuted antecedents. (Contributed by NM, 25-May-2005.) |
| Ref | Expression |
|---|---|
| imp.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| impcom | ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | imp.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 2 | 1 | com12 32 | . 2 ⊢ (𝜓 → (𝜑 → 𝜒)) |
| 3 | 2 | imp 406 | 1 ⊢ ((𝜓 ∧ 𝜑) → 𝜒) |
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