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| Mirrors > Home > MPE Home > Th. List > eximdv | Structured version Visualization version GIF version | ||
| Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1834. See eximdh 1864 and eximd 2216 for versions without a distinct variable condition. (Contributed by NM, 27-Apr-1994.) |
| Ref | Expression |
|---|---|
| alimdv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| eximdv | ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-5 1910 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
| 2 | alimdv.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 3 | 1, 2 | eximdh 1864 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
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