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Theorem nfn 1564
Description: Inference associated with nfnt 1562. (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 1562 . 2 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
31, 2ax-mp 7 1 𝑥 ¬ 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-nf 1366
This theorem is referenced by:  nfdc  1565  19.32dc  1585  nfnae  1626  mo2n  1944  nfne  2312  nfnel  2321  nfdif  3093  nfpo  4066  0neqopab  5578  nfsup  6398  oddpwdclemndvds  10259
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