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| Mirrors > Home > MPE Home > Th. List > rspa | Structured version Visualization version GIF version | ||
| Description: Restricted specialization. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
| Ref | Expression |
|---|---|
| rspa | ⊢ ((∀𝑥 ∈ 𝐴 𝜑 ∧ 𝑥 ∈ 𝐴) → 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rsp 3247 | . 2 ⊢ (∀𝑥 ∈ 𝐴 𝜑 → (𝑥 ∈ 𝐴 → 𝜑)) | |
| 2 | 1 | imp 406 | 1 ⊢ ((∀𝑥 ∈ 𝐴 𝜑 ∧ 𝑥 ∈ 𝐴) → 𝜑) |
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