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Theorem nex 1432
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 1431 . 2 (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2 nex.1 . 2 ¬ 𝜑
31, 2mpgbi 1384 1 ¬ ∃𝑥𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wex 1424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1379  ax-gen 1381  ax-ie2 1426
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293
This theorem is referenced by:  ru  2828  0nelxp  4436  0xp  4484  dm0  4616  co02  4906  0fv  5295  mpt20  5668  0npr  6978
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