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Theorem ifpid2 35861
Description: Restate wff as conditional logic operator. (Contributed by RP, 20-Apr-2020.)
Assertion
Ref Expression
ifpid2  |-  ( ph  <-> if- (
ph , T.  , F.  ) )

Proof of Theorem ifpid2
StepHypRef Expression
1 tru 1441 . . . 4  |- T.
21olci 392 . . 3  |-  ( -. 
ph  \/ T.  )
32biantrur 508 . 2  |-  ( (
ph  \/ F.  )  <->  ( ( -.  ph  \/ T.  )  /\  ( ph  \/ F.  ) ) )
4 fal 1444 . . 3  |-  -. F.
54biorfi 408 . 2  |-  ( ph  <->  (
ph  \/ F.  )
)
6 dfifp4 1424 . 2  |-  (if- (
ph , T.  , F.  )  <->  ( ( -. 
ph  \/ T.  )  /\  ( ph  \/ F.  ) ) )
73, 5, 63bitr4i 280 1  |-  ( ph  <-> if- (
ph , T.  , F.  ) )
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:  frege52aid  36139
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