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

Theorem nfn 1589
Description: Inference associated with nfnt 1587. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfn.1  |-  F/ x ph
Assertion
Ref Expression
nfn  |-  F/ x  -.  ph

Proof of Theorem nfn
StepHypRef Expression
1 nfn.1 . 2  |-  F/ x ph
2 nfnt 1587 . 2  |-  ( F/ x ph  ->  F/ x  -.  ph )
31, 2ax-mp 7 1  |-  F/ x  -.  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3   F/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:  nfdc  1590  19.32dc  1610  nfnae  1651  mo2n  1970  nfne  2338  nfnel  2347  nfdif  3094  nfpo  4064  0neqopab  5581  nfsup  6464  zsupcllemstep  10485  oddpwdclemndvds  10693
  Copyright terms: Public domain W3C validator