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Theorem nexd 2254
Description: Deduction for generalization rule for negated wff. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
nexd.1 𝑥𝜑
nexd.2 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
nexd (𝜑 → ¬ ∃𝑥𝜓)

Proof of Theorem nexd
StepHypRef Expression
1 nexd.1 . . 3 𝑥𝜑
21nf5ri 2227 . 2 (𝜑 → ∀𝑥𝜑)
3 nexd.2 . 2 (𝜑 → ¬ 𝜓)
42, 3nexdh 1962 1 (𝜑 → ¬ ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wex 1874  wnf 1878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-12 2211
This theorem depends on definitions:  df-bi 198  df-ex 1875  df-nf 1879
This theorem is referenced by:  axrepnd  9668  axunnd  9670
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