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| Mirrors > Home > MPE Home > Th. List > rexlimddv | Structured version Visualization version GIF version | ||
| Description: Restricted existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 15-Jun-2016.) |
| Ref | Expression |
|---|---|
| rexlimddv.1 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
| rexlimddv.2 | ⊢ ((𝜑 ∧ (𝑥 ∈ 𝐴 ∧ 𝜓)) → 𝜒) |
| Ref | Expression |
|---|---|
| rexlimddv | ⊢ (𝜑 → 𝜒) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rexlimddv.1 | . 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) | |
| 2 | rexlimddv.2 | . . 3 ⊢ ((𝜑 ∧ (𝑥 ∈ 𝐴 ∧ 𝜓)) → 𝜒) | |
| 3 | 2 | rexlimdvaa 3156 | . 2 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
| 4 | 1, 3 | mpd 15 | 1 ⊢ (𝜑 → 𝜒) |
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