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| Mirrors > Home > MPE Home > Th. List > rgenw | Structured version Visualization version GIF version | ||
| Description: Generalization rule for restricted quantification. (Contributed by NM, 18-Jun-2014.) |
| Ref | Expression |
|---|---|
| rgenw.1 | ⊢ 𝜑 |
| Ref | Expression |
|---|---|
| rgenw | ⊢ ∀𝑥 ∈ 𝐴 𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rgenw.1 | . . 3 ⊢ 𝜑 | |
| 2 | 1 | a1i 11 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝜑) |
| 3 | 2 | rgen 3063 | 1 ⊢ ∀𝑥 ∈ 𝐴 𝜑 |
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