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Theorem nex 1386
Description: Generalization rule for negated wff. (Contributed by NM, 18-May-1994.)
Hypothesis
Ref Expression
nex.1 ¬ φ
Assertion
Ref Expression
nex ¬ xφ

Proof of Theorem nex
StepHypRef Expression
1 alnex 1385 . 2 (x ¬ φ ↔ ¬ xφ)
2 nex.1 . 2 ¬ φ
31, 2mpgbi 1338 1 ¬ xφ
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wex 1378
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 1333  ax-gen 1335  ax-ie2 1380
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by:  ru  2757  0nelxp  4315  0xp  4363  dm0  4492  co02  4777  0fv  5151  mpt20  5516  0npr  6466
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