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| Mirrors > Home > MPE Home > Th. List > rexlimd | Structured version Visualization version GIF version | ||
| Description: Deduction form of rexlimd 3266. For a version based on fewer axioms see rexlimdv 3153. (Contributed by NM, 27-May-1998.) (Proof shortened by Andrew Salmon, 30-May-2011.) (Proof shortened by Wolf Lammen, 14-Jan-2020.) |
| Ref | Expression |
|---|---|
| rexlimd.1 | ⊢ Ⅎ𝑥𝜑 |
| rexlimd.2 | ⊢ Ⅎ𝑥𝜒 |
| rexlimd.3 | ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) |
| Ref | Expression |
|---|---|
| rexlimd | ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rexlimd.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
| 2 | rexlimd.2 | . . 3 ⊢ Ⅎ𝑥𝜒 | |
| 3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜒) |
| 4 | rexlimd.3 | . 2 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) | |
| 5 | 1, 3, 4 | rexlimd2 3265 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
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