MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfnd Structured version   Visualization version   GIF version

Theorem nfnd 1954
Description: Deduction associated with nfnt 1952. (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 1952 . 2 (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
31, 2syl 17 1 (𝜑 → Ⅎ𝑥 ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wnf 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904
This theorem depends on definitions:  df-bi 198  df-or 874  df-ex 1875  df-nf 1879
This theorem is referenced by:  nfand  1996  nfan1  2230  hbnt  2320  nfexd  2332  cbvexd  2381  nfexd2  2426  nfned  3038  nfneld  3048  nfrexd  3152  axpowndlem3  9678  axpowndlem4  9679  axregndlem2  9682  axregnd  9683  distel  32173  bj-cbvexdv  33191
  Copyright terms: Public domain W3C validator