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Theorem re1luk2 1466
Description: luk-2 1411 derived from the Tarski-Bernays-Wajsberg axioms. (Contributed by Anthony Hart, 16-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re1luk2  |-  ( ( -.  ph  ->  ph )  ->  ph )

Proof of Theorem re1luk2
StepHypRef Expression
1 tbw-negdf 1454 . . . 4  |-  ( ( ( -.  ph  ->  (
ph  ->  F.  ) )  ->  ( ( ( ph  ->  F.  )  ->  -.  ph )  ->  F.  )
)  ->  F.  )
2 tbw-ax2 1456 . . . . 5  |-  ( ( ( ( ph  ->  F.  )  ->  -.  ph )  ->  F.  )  ->  (
( -.  ph  ->  (
ph  ->  F.  ) )  ->  ( ( ( ph  ->  F.  )  ->  -.  ph )  ->  F.  )
) )
3 tbwlem4 1463 . . . . 5  |-  ( ( ( ( ( ph  ->  F.  )  ->  -.  ph )  ->  F.  )  ->  ( ( -.  ph  ->  ( ph  ->  F.  ) )  ->  (
( ( ph  ->  F.  )  ->  -.  ph )  ->  F.  ) ) )  ->  ( ( ( ( -.  ph  ->  (
ph  ->  F.  ) )  ->  ( ( ( ph  ->  F.  )  ->  -.  ph )  ->  F.  )
)  ->  F.  )  ->  ( ( ph  ->  F.  )  ->  -.  ph )
) )
42, 3ax-mp 8 . . . 4  |-  ( ( ( ( -.  ph  ->  ( ph  ->  F.  ) )  ->  (
( ( ph  ->  F.  )  ->  -.  ph )  ->  F.  ) )  ->  F.  )  ->  ( (
ph  ->  F.  )  ->  -. 
ph ) )
51, 4ax-mp 8 . . 3  |-  ( (
ph  ->  F.  )  ->  -. 
ph )
6 tbw-ax1 1455 . . 3  |-  ( ( ( ph  ->  F.  )  ->  -.  ph )  -> 
( ( -.  ph  ->  ph )  ->  (
( ph  ->  F.  )  ->  ph ) ) )
75, 6ax-mp 8 . 2  |-  ( ( -.  ph  ->  ph )  ->  ( ( ph  ->  F.  )  ->  ph ) )
8 tbw-ax3 1457 . 2  |-  ( ( ( ph  ->  F.  )  ->  ph )  ->  ph )
97, 8tbwsyl 1459 1  |-  ( ( -.  ph  ->  ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    F. wfal 1308
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
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