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Theorem nfnth 1876
Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.) df-nf 1858 changed. (Revised by Wolf Lammen, 12-Sep-2021.)
Hypothesis
Ref Expression
nfnth.1 ¬ 𝜑
Assertion
Ref Expression
nfnth 𝑥𝜑

Proof of Theorem nfnth
StepHypRef Expression
1 nfntht2 1868 . 2 (∀𝑥 ¬ 𝜑 → Ⅎ𝑥𝜑)
2 nfnth.1 . 2 ¬ 𝜑
31, 2mpg 1872 1 𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wnf 1856
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870
This theorem depends on definitions:  df-bi 197  df-or 827  df-ex 1853  df-nf 1858
This theorem is referenced by:  nffal  1880  nd1  9610  nd2  9611
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