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Theorem nex 1555
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 1543 . 2 (x ¬ φ ↔ ¬ xφ)
2 nex.1 . 2 ¬ φ
31, 2mpgbi 1549 1 ¬ xφ
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  ru  3045  0nel1c  4159  xp0r  4842  dm0  4918  co02  5092  co01  5093  nenpw1pwlem2  6085
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