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

Theorem nfnd 1825
 Description: Deduction associated with nfnt 1822. (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 1822 . 2 (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
31, 2syl 17 1 (𝜑 → Ⅎ𝑥 ¬ 𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  Ⅎwnf 1748 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777 This theorem depends on definitions:  df-bi 197  df-or 384  df-ex 1745  df-nf 1750 This theorem is referenced by:  nfand  1866  hbnt  2182  nfexd  2203  cbvexd  2314  nfexd2  2363  nfned  2924  nfneld  2934  nfrexd  3035  axpowndlem3  9459  axpowndlem4  9460  axregndlem2  9463  axregnd  9464  distel  31833  bj-cbvexdv  32861
 Copyright terms: Public domain W3C validator