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Theorem nexd 1763
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 1754 . 2  |-  ( ph  ->  A. x ph )
3 nexd.2 . 2  |-  ( ph  ->  -.  ps )
42, 3nexdh 1579 1  |-  ( ph  ->  -.  E. x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   E.wex 1531   F/wnf 1534
This theorem is referenced by:  nexdv  1869  axrepnd  8232  axunnd  8234
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-ex 1532  df-nf 1535
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