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Mirrors > Home > MPE Home > Th. List > nfnt | Structured version Visualization version GIF version |
Description: If a variable is non-free in a proposition, then it is non-free in its negation. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 28-Dec-2017.) (Revised by BJ, 24-Jul-2019.) df-nf 1747 changed. (Revised by Wolf Lammen, 4-Oct-2021.) |
Ref | Expression |
---|---|
nfnt | ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnbi 1817 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥 ¬ 𝜑) | |
2 | 1 | biimpi 208 | 1 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 Ⅎwnf 1746 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 |
This theorem depends on definitions: df-bi 199 df-or 834 df-ex 1743 df-nf 1747 |
This theorem is referenced by: nfn 1819 nfnd 1820 19.23tOLD 2140 wl-nfeqfb 34215 |
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