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Theorem nexd 1869
Description: Deduction for generalization rule for negated wff. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
nexd.1  |-  F/ x ph
nexd.2  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
nexd  |-  ( ph  ->  -.  E. x ps )

Proof of Theorem nexd
StepHypRef Expression
1 nexd.1 . . 3  |-  F/ x ph
21nfri 1860 . 2  |-  ( ph  ->  A. x ph )
3 nexd.2 . 2  |-  ( ph  ->  -.  ps )
42, 3nexdh 1661 1  |-  ( ph  ->  -.  E. x ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   E.wex 1599   F/wnf 1603
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-12 1840
This theorem depends on definitions:  df-bi 185  df-ex 1600  df-nf 1604
This theorem is referenced by:  nexdv  1870  axrepnd  8972  axunnd  8974
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