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Theorem nfnd 1783
Description: Deduction associated with nfnt 1780. (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 1780 . 2 (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
31, 2syl 17 1 (𝜑 → Ⅎ𝑥 ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wnf 1706
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735
This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1703  df-nf 1708
This theorem is referenced by:  nfand  1824  hbnt  2142  nfexd  2165  cbvexd  2276  nfexd2  2330  nfned  2892  nfneld  2902  nfrexd  3003  axpowndlem3  9406  axpowndlem4  9407  axregndlem2  9410  axregnd  9411  distel  31683  bj-cbvexdv  32711
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