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Theorem aisfina 37933
Description: Given a is equivalent to F., there exists a proof for not a. (Contributed by Jarvin Udandy, 30-Aug-2016.)
Hypothesis
Ref Expression
aisfina.1  |-  ( ph  <-> F.  )
Assertion
Ref Expression
aisfina  |-  -.  ph

Proof of Theorem aisfina
StepHypRef Expression
1 aisfina.1 . 2  |-  ( ph  <-> F.  )
2 nbfal 1448 . 2  |-  ( -. 
ph 
<->  ( ph  <-> F.  )
)
31, 2mpbir 212 1  |-  -.  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187   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-tru 1440  df-fal 1443
This theorem is referenced by:  aistbisfiaxb  37955  aisfbistiaxb  37956  aifftbifffaibif  37957  aifftbifffaibifff  37958  atnaiana  37959  dandysum2p2e4  38034
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