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| Mirrors > Home > MPE Home > Th. List > exlimddv | Structured version Visualization version GIF version | ||
| Description: Existential elimination rule of natural deduction (Rule C, explained in exlimiv 1930). (Contributed by Mario Carneiro, 15-Jun-2016.) |
| Ref | Expression |
|---|---|
| exlimddv.1 | ⊢ (𝜑 → ∃𝑥𝜓) |
| exlimddv.2 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
| Ref | Expression |
|---|---|
| exlimddv | ⊢ (𝜑 → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | exlimddv.1 | . 2 ⊢ (𝜑 → ∃𝑥𝜓) | |
| 2 | exlimddv.2 | . . . 4 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
| 3 | 2 | ex 412 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) |
| 4 | 3 | exlimdv 1933 | . 2 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
| 5 | 1, 4 | mpd 15 | 1 ⊢ (𝜑 → 𝜒) |
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