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Theorem pm2.01da 795
Description: Deduction based on reductio ad absurdum. See pm2.01 190. (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 413 . 2 (𝜑 → (𝜓 → ¬ 𝜓))
32pm2.01d 191 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 396
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 208  df-an 397
This theorem is referenced by:  efrirr  5529  omlimcl  8193  hartogslem1  8994  cfslb2n  9678  fin23lem41  9762  tskuni  10193  4sqlem18  16286  ramlb  16343  ivthlem2  23980  ivthlem3  23981  cosne0  25041  footne  26436  nsnlplig  28185  unbdqndv1  33744  unbdqndv2  33747  knoppndv  33770  fmtno4prm  43614
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