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Theorem nfnt 1933
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 1858 changed. (Revised by Wolf Lammen, 4-Oct-2021.)
Assertion
Ref Expression
nfnt (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)

Proof of Theorem nfnt
StepHypRef Expression
1 nfnbi 1931 . 2 (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥 ¬ 𝜑)
21biimpi 206 1 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wnf 1856
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885
This theorem depends on definitions:  df-bi 197  df-or 837  df-ex 1853  df-nf 1858
This theorem is referenced by:  nfn  1935  nfnd  1936  nfan1OLDOLD  2223  19.23t  2235  wl-nfnbi  33649  wl-nfeqfb  33658  19.9alt  34774
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