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Theorem pm3.44 687
Description: Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)
Assertion
Ref Expression
pm3.44  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  ->  ( ( ps  \/  ch )  ->  ph ) )

Proof of Theorem pm3.44
StepHypRef Expression
1 jaob 682 . 2  |-  ( ( ( ps  \/  ch )  ->  ph )  <->  ( ( ps  ->  ph )  /\  ( ch  ->  ph ) ) )
21biimpri 132 1  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  ->  ( ( ps  \/  ch )  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    \/ wo 680
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 681
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  jaoi  688  jao  727  pm2.6dc  830  pm4.83dc  918
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