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| Mirrors > Home > MPE Home > Th. List > nfra1 | Structured version Visualization version GIF version | ||
| Description: The setvar 𝑥 is not free in ∀𝑥 ∈ 𝐴𝜑. (Contributed by NM, 18-Oct-1996.) (Revised by Mario Carneiro, 7-Oct-2016.) |
| Ref | Expression |
|---|---|
| nfra1 | ⊢ Ⅎ𝑥∀𝑥 ∈ 𝐴 𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ral 3062 | . 2 ⊢ (∀𝑥 ∈ 𝐴 𝜑 ↔ ∀𝑥(𝑥 ∈ 𝐴 → 𝜑)) | |
| 2 | nfa1 2151 | . 2 ⊢ Ⅎ𝑥∀𝑥(𝑥 ∈ 𝐴 → 𝜑) | |
| 3 | 1, 2 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥∀𝑥 ∈ 𝐴 𝜑 |
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