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Theorem orfa 30406
Description: The falsum F. can be removed from a disjunction. (Contributed by Giovanni Mascellani, 15-Sep-2017.)
Assertion
Ref Expression
orfa  |-  ( (
ph  \/ F.  )  <->  ph )

Proof of Theorem orfa
StepHypRef Expression
1 orcom 387 . . . 4  |-  ( (
ph  \/ F.  )  <->  ( F.  \/  ph )
)
2 df-or 370 . . . 4  |-  ( ( F.  \/  ph )  <->  ( -. F.  ->  ph )
)
31, 2bitri 249 . . 3  |-  ( (
ph  \/ F.  )  <->  ( -. F.  ->  ph )
)
4 fal 1386 . . . 4  |-  -. F.
5 pm2.27 39 . . . 4  |-  ( -. F.  ->  ( ( -. F.  ->  ph )  ->  ph ) )
64, 5ax-mp 5 . . 3  |-  ( ( -. F.  ->  ph )  ->  ph )
73, 6sylbi 195 . 2  |-  ( (
ph  \/ F.  )  ->  ph )
8 orc 385 . 2  |-  ( ph  ->  ( ph  \/ F.  ) )
97, 8impbii 188 1  |-  ( (
ph  \/ F.  )  <->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ wo 368   F. wfal 1384
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 185  df-or 370  df-tru 1382  df-fal 1385
This theorem is referenced by: (None)
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