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Theorem nexd 1779
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 1770 . 2  |-  ( ph  ->  A. x ph )
3 nexd.2 . 2  |-  ( ph  ->  -.  ps )
42, 3nexdh 1596 1  |-  ( ph  ->  -.  E. x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   E.wex 1547   F/wnf 1550
This theorem is referenced by:  nexdv  1930  axrepnd  8395  axunnd  8397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-ex 1548  df-nf 1551
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