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Theorem pm4.78i 756
Description: Implication distributes over disjunction. One direction of Theorem *4.78 of [WhiteheadRussell] p. 121. The converse holds in classical logic. (Contributed by Jim Kingdon, 15-Jan-2018.)
Assertion
Ref Expression
pm4.78i  |-  ( ( ( ph  ->  ps )  \/  ( ph  ->  ch ) )  -> 
( ph  ->  ( ps  \/  ch ) ) )

Proof of Theorem pm4.78i
StepHypRef Expression
1 orc 686 . . 3  |-  ( ps 
->  ( ps  \/  ch ) )
21imim2i 12 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps  \/  ch ) ) )
3 olc 685 . . 3  |-  ( ch 
->  ( ps  \/  ch ) )
43imim2i 12 . 2  |-  ( (
ph  ->  ch )  -> 
( ph  ->  ( ps  \/  ch ) ) )
52, 4jaoi 690 1  |-  ( ( ( ph  ->  ps )  \/  ( ph  ->  ch ) )  -> 
( ph  ->  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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