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Theorem pm3.44 513
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 23 . 2  |-  ( ( ps  ->  ph )  -> 
( ps  ->  ph )
)
2 id 23 . 2  |-  ( ( ch  ->  ph )  -> 
( ch  ->  ph )
)
31, 2jaao 511 1  |-  ( ( ( ps  ->  ph )  /\  ( ch  ->  ph )
)  ->  ( ( ps  \/  ch )  ->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 369    /\ wa 370
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 188  df-or 371  df-an 372
This theorem is referenced by:  jao  514  jaob  790  dvmptconst  37357  dvmptidg  37359  dvmulcncf  37369  dvdivcncf  37371  fourierdlem101  37639
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