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Theorem nexdv 1853
Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
nexdv.1  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
nexdv  |-  ( ph  ->  -.  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem nexdv
StepHypRef Expression
1 ax-17 1460 . 2  |-  ( ph  ->  A. x ph )
2 nexdv.1 . 2  |-  ( ph  ->  -.  ps )
31, 2nexd 1545 1  |-  ( ph  ->  -.  E. x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ie2 1424  ax-17 1460
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291
This theorem is referenced by: (None)
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