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Theorem conimpfalt 27990
Description: Assuming a, not b, and a implies b, there exists a proof that a is false.) (Contributed by Jarvin Udandy, 29-Aug-2016.)
Hypotheses
Ref Expression
conimpfalt.1  |-  ph
conimpfalt.2  |-  -.  ps
conimpfalt.3  |-  ( ph  ->  ps )
Assertion
Ref Expression
conimpfalt  |-  ( ph  <->  F.  )

Proof of Theorem conimpfalt
StepHypRef Expression
1 conimpfalt.1 . . 3  |-  ph
2 conimpfalt.3 . . 3  |-  ( ph  ->  ps )
31, 2ax-mp 8 . 2  |-  ps
4 conimpfalt.2 . 2  |-  -.  ps
53, 4pm2.24ii 124 1  |-  ( ph  <->  F.  )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    F. wfal 1308
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
  Copyright terms: Public domain W3C validator