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Theorem conimpf 27554
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  |-  ph
conimpf.2  |-  -.  ps
conimpf.3  |-  ( ph  ->  ps )
Assertion
Ref Expression
conimpf  |-  ( ph  <->  F.  )

Proof of Theorem conimpf
StepHypRef Expression
1 conimpf.3 . 2  |-  ( ph  ->  ps )
2 conimpf.2 . 2  |-  -.  ps
31, 2aibnbaif 27543 1  |-  ( ph  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 177    F. wfal 1323
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
  Copyright terms: Public domain W3C validator