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Theorem aibnbaif 27543
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  |-  ( ph  ->  ps )
aibnbaif.2  |-  -.  ps
Assertion
Ref Expression
aibnbaif  |-  ( ph  <->  F.  )

Proof of Theorem aibnbaif
StepHypRef Expression
1 aibnbaif.1 . . 3  |-  ( ph  ->  ps )
2 aibnbaif.2 . . 3  |-  -.  ps
31, 2aibnbna 27542 . 2  |-  -.  ph
43bifal 1333 1  |-  ( ph  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177    F. wfal 1323
This theorem is referenced by:  conimpf  27554  conimpfalt  27555  dandysum2p2e4  27611
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-tru 1325  df-fal 1326
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