ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nexdv Unicode version

Theorem nexdv 1888
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 1491 . 2  |-  ( ph  ->  A. x ph )
2 nexdv.1 . 2  |-  ( ph  ->  -.  ps )
31, 2nexd 1577 1  |-  ( ph  ->  -.  E. x ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   E.wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-5 1408  ax-gen 1410  ax-ie2 1455  ax-17 1491
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator