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Mirrors > Home > MPE Home > Th. List > nfv | Structured version Visualization version GIF version |
Description: If 𝑥 is not present in 𝜑, then 𝑥 is not free in 𝜑. (Contributed by Mario Carneiro, 11-Aug-2016.) Definition change. (Revised by Wolf Lammen, 12-Sep-2021.) |
Ref | Expression |
---|---|
nfv | ⊢ Ⅎ𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax5e 1829 | . . 3 ⊢ (∃𝑥𝜑 → 𝜑) | |
2 | ax-5 1827 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
3 | 1, 2 | syl 17 | . 2 ⊢ (∃𝑥𝜑 → ∀𝑥𝜑) |
4 | 3 | nfi 1705 | 1 ⊢ Ⅎ𝑥𝜑 |
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