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Theorem nfn 1621
Description: Inference associated with nfnt 1619. (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 1619 . 2 (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑)
31, 2ax-mp 5 1 𝑥 ¬ 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wnf 1421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-5 1408  ax-gen 1410  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322  df-nf 1422
This theorem is referenced by:  nfdc  1622  19.32dc  1642  nfnae  1685  mo2n  2005  nfne  2378  nfnel  2387  nfdif  3167  nfpo  4193  0neqopab  5784  nfsup  6847  ismkvnex  6997  mkvprop  7000  zsupcllemstep  11565  oddpwdclemndvds  11776
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