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Theorem nex 1389
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 1388 . 2 (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2 nex.1 . 2 ¬ 𝜑
31, 2mpgbi 1341 1 ¬ ∃𝑥𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wex 1381
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 1336  ax-gen 1338  ax-ie2 1383
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249
This theorem is referenced by:  ru  2763  0nelxp  4372  0xp  4420  dm0  4549  co02  4834  0fv  5208  mpt20  5574  0npr  6581
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