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Theorem nexdv 1827
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 1435 . 2 (𝜑 → ∀𝑥𝜑)
2 nexdv.1 . 2 (𝜑 → ¬ 𝜓)
31, 2nexd 1520 1 (𝜑 → ¬ ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-gen 1354  ax-ie2 1399  ax-17 1435
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by: (None)
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