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Theorem aifftbifffaibif 38222
Description: Given a is equivalent to T., Given b is equivalent to F., there exists a proof for that a implies b is false. (Contributed by Jarvin Udandy, 7-Sep-2020.)
Hypotheses
Ref Expression
aifftbifffaibif.1  |-  ( ph  <-> T.  )
aifftbifffaibif.2  |-  ( ps  <-> F.  )
Assertion
Ref Expression
aifftbifffaibif  |-  ( (
ph  ->  ps )  <-> F.  )

Proof of Theorem aifftbifffaibif
StepHypRef Expression
1 aifftbifffaibif.1 . . . . 5  |-  ( ph  <-> T.  )
21aistia 38197 . . . 4  |-  ph
3 aifftbifffaibif.2 . . . . 5  |-  ( ps  <-> F.  )
43aisfina 38198 . . . 4  |-  -.  ps
52, 4pm3.2i 456 . . 3  |-  ( ph  /\ 
-.  ps )
6 annim 426 . . . 4  |-  ( (
ph  /\  -.  ps )  <->  -.  ( ph  ->  ps ) )
76biimpi 197 . . 3  |-  ( (
ph  /\  -.  ps )  ->  -.  ( ph  ->  ps ) )
85, 7ax-mp 5 . 2  |-  -.  ( ph  ->  ps )
98bifal 1450 1  |-  ( (
ph  ->  ps )  <-> F.  )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    /\ wa 370   T. wtru 1438   F. wfal 1442
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 188  df-an 372  df-tru 1440  df-fal 1443
This theorem is referenced by:  atnaiana  38224
  Copyright terms: Public domain W3C validator