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Theorem nexdh 1576
Description: Deduction for generalization rule for negated wff. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
nexdh.1  |-  ( ph  ->  A. x ph )
nexdh.2  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
nexdh  |-  ( ph  ->  -.  E. x ps )

Proof of Theorem nexdh
StepHypRef Expression
1 nexdh.1 . . 3  |-  ( ph  ->  A. x ph )
2 nexdh.2 . . 3  |-  ( ph  ->  -.  ps )
31, 2alrimih 1552 . 2  |-  ( ph  ->  A. x  -.  ps )
4 alnex 1530 . 2  |-  ( A. x  -.  ps  <->  -.  E. x ps )
53, 4sylib 188 1  |-  ( ph  ->  -.  E. x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  nexd  1751
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-ex 1529
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