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Theorem pm2.01da 458
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
pm2.01da.1 ((𝜑𝜓) → ¬ 𝜓)
Assertion
Ref Expression
pm2.01da (𝜑 → ¬ 𝜓)

Proof of Theorem pm2.01da
StepHypRef Expression
1 pm2.01da.1 . . 3 ((𝜑𝜓) → ¬ 𝜓)
21ex 450 . 2 (𝜑 → (𝜓 → ¬ 𝜓))
32pm2.01d 181 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 384
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 197  df-an 386
This theorem is referenced by:  efrirr  5093  omlimcl  7655  hartogslem1  8444  cfslb2n  9087  fin23lem41  9171  tskuni  9602  4sqlem18  15660  ramlb  15717  ivthlem2  23215  ivthlem3  23216  cosne0  24270  footne  25609  nsnlplig  27317  unbdqndv1  32483  unbdqndv2  32486  knoppndv  32509  fmtno4prm  41258
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