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Theorem pm4.78i 819
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 643 . . 3  |-  ( ps 
->  ( ps  \/  ch ) )
21imim2i 12 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps  \/  ch ) ) )
3 olc 642 . . 3  |-  ( ch 
->  ( ps  \/  ch ) )
43imim2i 12 . 2  |-  ( (
ph  ->  ch )  -> 
( ph  ->  ( ps  \/  ch ) ) )
52, 4jaoi 646 1  |-  ( ( ( ph  ->  ps )  \/  ( ph  ->  ch ) )  -> 
( ph  ->  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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