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Theorem imimorb 847
Description: Simplify an implication between implications. (Contributed by Paul Chapman, 17-Nov-2012.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)
Assertion
Ref Expression
imimorb  |-  ( ( ( ps  ->  ch )  ->  ( ph  ->  ch ) )  <->  ( ph  ->  ( ps  \/  ch ) ) )

Proof of Theorem imimorb
StepHypRef Expression
1 bi2.04 350 . 2  |-  ( ( ( ps  ->  ch )  ->  ( ph  ->  ch ) )  <->  ( ph  ->  ( ( ps  ->  ch )  ->  ch )
) )
2 dfor2 400 . . 3  |-  ( ( ps  \/  ch )  <->  ( ( ps  ->  ch )  ->  ch ) )
32imbi2i 303 . 2  |-  ( (
ph  ->  ( ps  \/  ch ) )  <->  ( ph  ->  ( ( ps  ->  ch )  ->  ch )
) )
41, 3bitr4i 243 1  |-  ( ( ( ps  ->  ch )  ->  ( ph  ->  ch ) )  <->  ( ph  ->  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    \/ wo 357
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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