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Theorem inegd 1658
Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
inegd.1 ((𝜑𝜓) → ⊥)
Assertion
Ref Expression
inegd (𝜑 → ¬ 𝜓)

Proof of Theorem inegd
StepHypRef Expression
1 inegd.1 . . 3 ((𝜑𝜓) → ⊥)
21ex 399 . 2 (𝜑 → (𝜓 → ⊥))
3 dfnot 1657 . 2 𝜓 ↔ (𝜓 → ⊥))
42, 3sylibr 225 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 384  wfal 1650
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-an 385  df-tru 1641  df-fal 1651
This theorem is referenced by:  efald  1659  tglndim0  25734  archiabllem2c  30070
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