ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nex GIF version

Theorem nex 1405
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 1404 . 2 (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑)
2 nex.1 . 2 ¬ 𝜑
31, 2mpgbi 1357 1 ¬ ∃𝑥𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ie2 1399
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by:  ru  2785  0nelxp  4399  0xp  4447  dm0  4576  co02  4861  0fv  5235  mpt20  5601  0npr  6638
  Copyright terms: Public domain W3C validator