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Theorem nex 1405
Description: Generalization rule for negated wff. (Contributed by NM, 18-May-1994.)
Hypothesis
Ref Expression
nex.1  |-  -.  ph
Assertion
Ref Expression
nex  |-  -.  E. x ph

Proof of Theorem nex
StepHypRef Expression
1 alnex 1404 . 2  |-  ( A. x  -.  ph  <->  -.  E. x ph )
2 nex.1 . 2  |-  -.  ph
31, 2mpgbi 1357 1  |-  -.  E. x ph
Colors of variables: wff set class
Syntax hints:   -. wn 3   E.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  2786  0nelxp  4400  0xp  4448  dm0  4577  co02  4862  0fv  5236  mpt20  5602  0npr  6639
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