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Theorem dfifp4 1392
Description: Alternate definition of the conditional operator for propositions. (Contributed by BJ, 30-Sep-2019.)
Assertion
Ref Expression
dfifp4  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( -. 
ph  \/  ps )  /\  ( ph  \/  ch ) ) )

Proof of Theorem dfifp4
StepHypRef Expression
1 dfifp3 1391 . 2  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( ph  ->  ps )  /\  ( ph  \/  ch ) ) )
2 imor 412 . . 3  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
32anbi1i 695 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ph  \/  ch ) )  <->  ( ( -.  ph  \/  ps )  /\  ( ph  \/  ch ) ) )
41, 3bitri 251 1  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( -. 
ph  \/  ps )  /\  ( ph  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 186    \/ wo 368    /\ wa 369  if-wif 1388
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 187  df-or 370  df-an 371  df-ifp 1389
This theorem is referenced by:  anifp  1396  ifpan123g  35562  ifpan23  35563  ifpdfor2  35564  ifpdfor  35568  ifpim1  35572  ifpnot  35573  ifpid2  35574  ifpim2  35575  ifpnot23  35582  ifpidg  35595  ifpim123g  35604  ifpimim  35613
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