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| Mirrors > Home > MPE Home > Th. List > exlimdv | Structured version Visualization version GIF version | ||
| Description: Deduction form of Theorem 19.23 of [Margaris] p. 90, see 19.23 2211. (Contributed by NM, 27-Apr-1994.) Remove dependencies on ax-6 1967, ax-7 2007. (Revised by Wolf Lammen, 4-Dec-2017.) |
| Ref | Expression |
|---|---|
| exlimdv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
| Ref | Expression |
|---|---|
| exlimdv | ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | exlimdv.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 2 | 1 | eximdv 1917 | . 2 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
| 3 | ax5e 1912 | . 2 ⊢ (∃𝑥𝜒 → 𝜒) | |
| 4 | 2, 3 | syl6 35 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
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