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Theorem nfn 1594
Description: Inference associated with nfnt 1592. (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 1592 . 2 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
31, 2ax-mp 7 1 𝑥 ¬ 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wnf 1395
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-5 1382  ax-gen 1384  ax-ie2 1429  ax-4 1446  ax-ial 1473
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-fal 1296  df-nf 1396
This theorem is referenced by:  nfdc  1595  19.32dc  1615  nfnae  1658  mo2n  1977  nfne  2349  nfnel  2358  nfdif  3122  nfpo  4137  0neqopab  5708  nfsup  6741  zsupcllemstep  11280  oddpwdclemndvds  11488
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