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| Mirrors > Home > MPE Home > Th. List > impel | Structured version Visualization version GIF version | ||
| Description: An inference for implication elimination. (Contributed by Giovanni Mascellani, 23-May-2019.) (Proof shortened by Wolf Lammen, 2-Sep-2020.) |
| Ref | Expression |
|---|---|
| impel.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| impel.2 | ⊢ (𝜃 → 𝜓) |
| Ref | Expression |
|---|---|
| impel | ⊢ ((𝜑 ∧ 𝜃) → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | impel.2 | . . 3 ⊢ (𝜃 → 𝜓) | |
| 2 | impel.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 3 | 1, 2 | syl5 34 | . 2 ⊢ (𝜑 → (𝜃 → 𝜒)) |
| 4 | 3 | imp 406 | 1 ⊢ ((𝜑 ∧ 𝜃) → 𝜒) |
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