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Theorem nfn 1593
Description: Inference associated with nfnt 1591. (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 1591 . 2 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
31, 2ax-mp 7 1 𝑥 ¬ 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wnf 1394
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 579  ax-in2 580  ax-5 1381  ax-gen 1383  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395
This theorem is referenced by:  nfdc  1594  19.32dc  1614  nfnae  1657  mo2n  1976  nfne  2348  nfnel  2357  nfdif  3119  nfpo  4119  0neqopab  5676  nfsup  6666  zsupcllemstep  11034  oddpwdclemndvds  11242
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