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Theorem nexd 1575
Description: Deduction for generalization rule for negated wff. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
nexd.1  |-  ( ph  ->  A. x ph )
nexd.2  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
nexd  |-  ( ph  ->  -.  E. x ps )

Proof of Theorem nexd
StepHypRef Expression
1 nexd.1 . . 3  |-  ( ph  ->  A. x ph )
2 nexd.2 . . 3  |-  ( ph  ->  -.  ps )
31, 2alrimih 1428 . 2  |-  ( ph  ->  A. x  -.  ps )
4 alnex 1458 . 2  |-  ( A. x  -.  ps  <->  -.  E. x ps )
53, 4sylib 121 1  |-  ( ph  ->  -.  E. x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1312   E.wex 1451
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-ie2 1453
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320
This theorem is referenced by:  nexdv  1886
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