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Theorem nfnd 1668
Description: Deduction associated with nfnt 1667. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
nfnd.1 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfnd (𝜑 → Ⅎ𝑥 ¬ 𝜓)

Proof of Theorem nfnd
StepHypRef Expression
1 nfnd.1 . 2 (𝜑 → Ⅎ𝑥𝜓)
2 nfnt 1667 . 2 (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
31, 2syl 14 1 (𝜑 → Ⅎ𝑥 ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wnf 1471
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1458  ax-gen 1460  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-nf 1472
This theorem is referenced by:  nfned  2454  nfneld  2463  nfifd  3576
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