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Theorem nfn 1548
Description: Inference associated with nfnt 1546. (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 1546 . 2 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
31, 2ax-mp 7 1 𝑥 ¬ 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wnf 1349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350
This theorem is referenced by:  nfdc  1549  19.32dc  1569  nfnae  1610  mo2n  1928  nfne  2297  nfnel  2304  nfdif  3065  nfpo  4038  0neqopab  5550
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