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Theorem nex 1480
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 1479 . 2 (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2 nex.1 . 2 ¬ 𝜑
31, 2mpgbi 1432 1 ¬ ∃𝑥𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wex 1472
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 604  ax-in2 605  ax-5 1427  ax-gen 1429  ax-ie2 1474
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341
This theorem is referenced by:  ru  2936  0nelxp  4615  0xp  4667  dm0  4801  co02  5100  0fv  5504  mpo0  5892  0npr  7404
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