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Theorem conimpf 41830
Description: Assuming a, not b, and a implies b, there exists a proof that a is false.) (Contributed by Jarvin Udandy, 28-Aug-2016.)
Hypotheses
Ref Expression
conimpf.1 𝜑
conimpf.2 ¬ 𝜓
conimpf.3 (𝜑𝜓)
Assertion
Ref Expression
conimpf (𝜑 ↔ ⊥)

Proof of Theorem conimpf
StepHypRef Expression
1 conimpf.3 . 2 (𝜑𝜓)
2 conimpf.2 . 2 ¬ 𝜓
31, 2aibnbaif 41820 1 (𝜑 ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 198  wfal 1666
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 199  df-tru 1657  df-fal 1667
This theorem is referenced by: (None)
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