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Theorem pm3.44 668
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 664 . 2  |-  ( ( ( ps  \/  ch )  ->  ph )  <->  ( ( ps  ->  ph )  /\  ( ch  ->  ph ) ) )
21biimpri 131 1  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  ->  ( ( ps  \/  ch )  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    \/ wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  jaoi  669  jao  705  pm2.6dc  793  pm4.83dc  893
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