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

Theorem nfn 1636
 Description: Inference associated with nfnt 1634. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfn.1 𝑥𝜑
Assertion
Ref Expression
nfn 𝑥 ¬ 𝜑

Proof of Theorem nfn
StepHypRef Expression
1 nfn.1 . 2 𝑥𝜑
2 nfnt 1634 . 2 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
31, 2ax-mp 5 1 𝑥 ¬ 𝜑
 Colors of variables: wff set class Syntax hints:  ¬ wn 3  Ⅎwnf 1436 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie2 1470  ax-4 1487  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437 This theorem is referenced by:  nfdc  1637  19.32dc  1657  nfnae  1700  mo2n  2025  nfne  2399  nfnel  2408  nfdif  3192  nfpo  4218  0neqopab  5809  nfsup  6872  ismkvnex  7022  mkvprop  7025  zsupcllemstep  11627  oddpwdclemndvds  11838
 Copyright terms: Public domain W3C validator