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Theorem aisfina 27969
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 1316 . . . 4  |-  ( -. 
ph 
<->  ( ph  <->  F.  )
)
3 bicom 191 . . . . 5  |-  ( ( -.  ph  <->  ( ph  <->  F.  )
)  <->  ( ( ph  <->  F.  )  <->  -.  ph ) )
43biimpi 186 . . . 4  |-  ( ( -.  ph  <->  ( ph  <->  F.  )
)  ->  ( ( ph 
<->  F.  )  <->  -.  ph )
)
52, 4ax-mp 8 . . 3  |-  ( (
ph 
<->  F.  )  <->  -.  ph )
65biimpi 186 . 2  |-  ( (
ph 
<->  F.  )  ->  -.  ph )
71, 6ax-mp 8 1  |-  -.  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    F. wfal 1308
This theorem is referenced by:  bothfbothsame  27971  aibnbna  27977  aistbisfiaxb  27991  aisfbistiaxb  27992  dandysum2p2e4  28046
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 177  df-tru 1310  df-fal 1311
  Copyright terms: Public domain W3C validator