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Theorem orimdi 820
Description: Disjunction distributes over implication. (Contributed by Wolf Lammen, 5-Jan-2013.)
Assertion
Ref Expression
orimdi  |-  ( (
ph  \/  ( ps  ->  ch ) )  <->  ( ( ph  \/  ps )  -> 
( ph  \/  ch ) ) )

Proof of Theorem orimdi
StepHypRef Expression
1 imdi 352 . 2  |-  ( ( -.  ph  ->  ( ps 
->  ch ) )  <->  ( ( -.  ph  ->  ps )  ->  ( -.  ph  ->  ch ) ) )
2 df-or 359 . 2  |-  ( (
ph  \/  ( ps  ->  ch ) )  <->  ( -.  ph 
->  ( ps  ->  ch ) ) )
3 df-or 359 . . 3  |-  ( (
ph  \/  ps )  <->  ( -.  ph  ->  ps )
)
4 df-or 359 . . 3  |-  ( (
ph  \/  ch )  <->  ( -.  ph  ->  ch )
)
53, 4imbi12i 316 . 2  |-  ( ( ( ph  \/  ps )  ->  ( ph  \/  ch ) )  <->  ( ( -.  ph  ->  ps )  ->  ( -.  ph  ->  ch ) ) )
61, 2, 53bitr4i 268 1  |-  ( (
ph  \/  ( ps  ->  ch ) )  <->  ( ( ph  \/  ps )  -> 
( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357
This theorem is referenced by:  pm2.76  821  pm2.85  826
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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