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Theorem pm2.18da 799
Description: Deduction based on reductio ad absurdum. See pm2.18 128. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
pm2.18da.1 ((𝜑 ∧ ¬ 𝜓) → 𝜓)
Assertion
Ref Expression
pm2.18da (𝜑𝜓)

Proof of Theorem pm2.18da
StepHypRef Expression
1 pm2.18da.1 . . 3 ((𝜑 ∧ ¬ 𝜓) → 𝜓)
21ex 416 . 2 (𝜑 → (¬ 𝜓𝜓))
32pm2.18d 127 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 399
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 210  df-an 400
This theorem is referenced by:  fpwwe2lem13  10062  bpos  25880  tocyccntz  30818  2pwp1prm  44032
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