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Theorem nexdv 1808
Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
nexdv.1 (φ → ¬ ψ)
Assertion
Ref Expression
nexdv (φ → ¬ xψ)
Distinct variable group:   φ,x
Allowed substitution hint:   ψ(x)

Proof of Theorem nexdv
StepHypRef Expression
1 ax-17 1416 . 2 (φxφ)
2 nexdv.1 . 2 (φ → ¬ ψ)
31, 2nexd 1501 1 (φ → ¬ xψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-17 1416
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by: (None)
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