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Theorem ifpdfor 35807
Description: Define or in terms of conditional logic operator and true. (Contributed by RP, 20-Apr-2020.)
Assertion
Ref Expression
ifpdfor  |-  ( (
ph  \/  ps )  <-> if- (
ph , T.  ,  ps ) )

Proof of Theorem ifpdfor
StepHypRef Expression
1 tru 1441 . . . 4  |- T.
21olci 392 . . 3  |-  ( -. 
ph  \/ T.  )
32biantrur 508 . 2  |-  ( (
ph  \/  ps )  <->  ( ( -.  ph  \/ T.  )  /\  ( ph  \/  ps ) ) )
4 dfifp4 1424 . 2  |-  (if- (
ph , T.  ,  ps )  <->  ( ( -. 
ph  \/ T.  )  /\  ( ph  \/  ps ) ) )
53, 4bitr4i 255 1  |-  ( (
ph  \/  ps )  <-> if- (
ph , T.  ,  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ wo 369    /\ wa 370  if-wif 1420   T. wtru 1438
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
This theorem is referenced by:  ifpdfxor  35830
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