ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfnd GIF version

Theorem nfnd 1588
Description: Deduction associated with nfnt 1587. (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 1587 . 2 (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓)
31, 2syl 14 1 (𝜑 → Ⅎ𝑥 ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wnf 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391
This theorem is referenced by:  nfned  2343  nfneld  2352  nfifd  3393
  Copyright terms: Public domain W3C validator