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Theorem nrex 3074
Description: Inference adding restricted existential quantifier to negated wff. (Contributed by NM, 16-Oct-2003.)
Hypothesis
Ref Expression
nrex.1 (𝑥𝐴 → ¬ 𝜓)
Assertion
Ref Expression
nrex ¬ ∃𝑥𝐴 𝜓

Proof of Theorem nrex
StepHypRef Expression
1 nrex.1 . . 3 (𝑥𝐴 → ¬ 𝜓)
21rgen 3063 . 2 𝑥𝐴 ¬ 𝜓
3 ralnex 3072 . 2 (∀𝑥𝐴 ¬ 𝜓 ↔ ¬ ∃𝑥𝐴 𝜓)
42, 3mpbi 229 1 ¬ ∃𝑥𝐴 𝜓
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2107  wral 3061  wrex 3070
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-ral 3062  df-rex 3071
This theorem is referenced by:  rex0  4318  iun0  5023  canth  7311  orduninsuc  7780  wfrlem16OLD  8271  wofib  9486  cfsuc  10198  nominpos  12395  nnunb  12414  indstr  12846  eirr  16092  sqrt2irr  16136  vdwap0  16853  smndex1n0mnd  18727  smndex2dnrinv  18730  psgnunilem3  19283  bwth  22777  zfbas  23263  aaliou3lem9  25726  vma1  26531  muls01  27397  mulsrid  27399  hatomistici  31346  esumrnmpt2  32724  fmlan0  34042  linedegen  34774  limsucncmpi  34963  elpadd0  38318  rexanuz2nf  43814  fourierdlem62  44495  etransc  44610  0nodd  46190  2nodd  46192  1neven  46316
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