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Theorem dfifp5 1425
Description: Alternate definition of the conditional operator for propositions. (Contributed by BJ, 2-Oct-2019.)
Assertion
Ref Expression
dfifp5  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( -. 
ph  \/  ps )  /\  ( -.  ph  ->  ch ) ) )

Proof of Theorem dfifp5
StepHypRef Expression
1 dfifp2 1422 . 2  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( ph  ->  ps )  /\  ( -.  ph  ->  ch )
) )
2 imor 413 . . 3  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
32anbi1i 699 . 2  |-  ( ( ( ph  ->  ps )  /\  ( -.  ph  ->  ch ) )  <->  ( ( -.  ph  \/  ps )  /\  ( -.  ph  ->  ch ) ) )
41, 3bitri 252 1  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( -. 
ph  \/  ps )  /\  ( -.  ph  ->  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    \/ wo 369    /\ wa 370  if-wif 1420
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
This theorem is referenced by: (None)
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