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Theorem aibnbaif 43941
Description: Given a implies b, not b, there exists a proof for a is F. (Contributed by Jarvin Udandy, 1-Sep-2016.)
Hypotheses
Ref Expression
aibnbaif.1 (𝜑𝜓)
aibnbaif.2 ¬ 𝜓
Assertion
Ref Expression
aibnbaif (𝜑 ↔ ⊥)

Proof of Theorem aibnbaif
StepHypRef Expression
1 aibnbaif.1 . . 3 (𝜑𝜓)
2 aibnbaif.2 . . 3 ¬ 𝜓
31, 2aibnbna 43940 . 2 ¬ 𝜑
43bifal 1558 1 (𝜑 ↔ ⊥)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 209  wfal 1554
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-tru 1545  df-fal 1555
This theorem is referenced by:  conimpf  43951  conimpfalt  43952  dandysum2p2e4  44032
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