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Theorem dfifp7 1427
Description: Alternate definition of the conditional operator for propositions. (Contributed by BJ, 2-Oct-2019.)
Assertion
Ref Expression
dfifp7  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( ch 
->  ph )  ->  ( ph  /\  ps ) ) )

Proof of Theorem dfifp7
StepHypRef Expression
1 orcom 388 . 2  |-  ( ( ( ph  /\  ps )  \/  -.  ( ch  ->  ph ) )  <->  ( -.  ( ch  ->  ph )  \/  ( ph  /\  ps ) ) )
2 dfifp6 1426 . 2  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( ph  /\ 
ps )  \/  -.  ( ch  ->  ph )
) )
3 imor 413 . 2  |-  ( ( ( ch  ->  ph )  ->  ( ph  /\  ps ) )  <->  ( -.  ( ch  ->  ph )  \/  ( ph  /\  ps ) ) )
41, 2, 33bitr4i 280 1  |-  (if- (
ph ,  ps ,  ch )  <->  ( ( ch 
->  ph )  ->  ( ph  /\  ps ) ) )
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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