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Theorem nexd 2127
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 2103 . 2 (𝜑 → ∀𝑥𝜑)
3 nexd.2 . 2 (𝜑 → ¬ 𝜓)
42, 3nexdh 1832 1 (𝜑 → ¬ ∃𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wex 1744  wnf 1748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745  df-nf 1750
This theorem is referenced by:  axrepnd  9454  axunnd  9456
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