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Theorem pm3.44 499
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 id 21 . 2  |-  ( ( ps  ->  ph )  -> 
( ps  ->  ph )
)
2 id 21 . 2  |-  ( ( ch  ->  ph )  -> 
( ch  ->  ph )
)
31, 2jaao 497 1  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  ->  ( ( ps  \/  ch )  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359    /\ wa 360
This theorem is referenced by:  jao  500  jaob  761
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362
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