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| Mirrors > Home > MPE Home > Th. List > mpjaodan | Structured version Visualization version GIF version | ||
| Description: Eliminate a disjunction in a deduction. A translation of natural deduction rule ∨ E (∨ elimination), see natded 30422. (Contributed by Mario Carneiro, 29-May-2016.) |
| Ref | Expression |
|---|---|
| jaodan.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| jaodan.2 | ⊢ ((𝜑 ∧ 𝜃) → 𝜒) |
| jaodan.3 | ⊢ (𝜑 → (𝜓 ∨ 𝜃)) |
| Ref | Expression |
|---|---|
| mpjaodan | ⊢ (𝜑 → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jaodan.3 | . 2 ⊢ (𝜑 → (𝜓 ∨ 𝜃)) | |
| 2 | jaodan.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 3 | jaodan.2 | . . 3 ⊢ ((𝜑 ∧ 𝜃) → 𝜒) | |
| 4 | 2, 3 | jaodan 960 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∨ 𝜃)) → 𝜒) |
| 5 | 1, 4 | mpdan 687 | 1 ⊢ (𝜑 → 𝜒) |
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