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Theorem efald 1659
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
efald.1 ((𝜑 ∧ ¬ 𝜓) → ⊥)
Assertion
Ref Expression
efald (𝜑𝜓)

Proof of Theorem efald
StepHypRef Expression
1 efald.1 . . 3 ((𝜑 ∧ ¬ 𝜓) → ⊥)
21inegd 1658 . 2 (𝜑 → ¬ ¬ 𝜓)
32notnotrd 130 1 (𝜑𝜓)
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:  efald2  34206
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