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Theorem ifpnot 35860
Description: Restate negated wff as conditional logic operator. (Contributed by RP, 20-Apr-2020.)
Assertion
Ref Expression
ifpnot  |-  ( -. 
ph 
<-> if- ( ph , F.  , T.  ) )

Proof of Theorem ifpnot
StepHypRef Expression
1 tru 1441 . . . 4  |- T.
21olci 392 . . 3  |-  ( ph  \/ T.  )
32biantru 507 . 2  |-  ( ( -.  ph  \/ F.  ) 
<->  ( ( -.  ph  \/ F.  )  /\  ( ph  \/ T.  ) ) )
4 fal 1444 . . 3  |-  -. F.
54biorfi 408 . 2  |-  ( -. 
ph 
<->  ( -.  ph  \/ F.  ) )
6 dfifp4 1424 . 2  |-  (if- (
ph , F.  , T.  )  <->  ( ( -. 
ph  \/ F.  )  /\  ( ph  \/ T.  ) ) )
73, 5, 63bitr4i 280 1  |-  ( -. 
ph 
<-> if- ( ph , F.  , T.  ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ wo 369    /\ wa 370  if-wif 1420   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-or 371  df-an 372  df-ifp 1421  df-tru 1440  df-fal 1443
This theorem is referenced by: (None)
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