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Theorem pm3.44 509
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 22 . 2  |-  ( ( ps  ->  ph )  -> 
( ps  ->  ph )
)
2 id 22 . 2  |-  ( ( ch  ->  ph )  -> 
( ch  ->  ph )
)
31, 2jaao 507 1  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  ->  ( ( ps  \/  ch )  ->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 366    /\ wa 367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369
This theorem is referenced by:  jao  510  jaob  781  dvmptconst  31952  dvmptidg  31954  dvmulcncf  31964  dvdivcncf  31966  fourierdlem101  32232
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