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Theorem rb-imdf 1505
Description: The definition of implication, in terms of  \/ and  -.. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rb-imdf  |-  -.  ( -.  ( -.  ( ph  ->  ps )  \/  ( -.  ph  \/  ps )
)  \/  -.  ( -.  ( -.  ph  \/  ps )  \/  ( ph  ->  ps ) ) )

Proof of Theorem rb-imdf
StepHypRef Expression
1 imor 401 . 2  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
2 rb-bijust 1504 . 2  |-  ( ( ( ph  ->  ps ) 
<->  ( -.  ph  \/  ps ) )  <->  -.  ( -.  ( -.  ( ph  ->  ps )  \/  ( -.  ph  \/  ps )
)  \/  -.  ( -.  ( -.  ph  \/  ps )  \/  ( ph  ->  ps ) ) ) )
31, 2mpbi 199 1  |-  -.  ( -.  ( -.  ( ph  ->  ps )  \/  ( -.  ph  \/  ps )
)  \/  -.  ( -.  ( -.  ph  \/  ps )  \/  ( ph  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357
This theorem is referenced by:  re1axmp  1519  re2luk1  1520  re2luk2  1521  re2luk3  1522
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
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