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Theorem dfifp4 1425
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 1424 . 2  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( ph  ->  ps )  /\  ( ph  \/  ch ) ) )
2 imor 414 . . 3  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
32anbi1i 700 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ph  \/  ch ) )  <->  ( ( -.  ph  \/  ps )  /\  ( ph  \/  ch ) ) )
41, 3bitri 253 1  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( -. 
ph  \/  ps )  /\  ( ph  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 188    \/ wo 370    /\ wa 371  if-wif 1421
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 189  df-or 372  df-an 373  df-ifp 1422
This theorem is referenced by:  anifp  1429  ifpan123g  36028  ifpan23  36029  ifpdfor2  36030  ifpdfor  36034  ifpim1  36038  ifpnot  36039  ifpid2  36040  ifpim2  36041  ifpnot23  36048  ifpidg  36061  ifpim123g  36070  ifpimim  36079
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