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Theorem pm3.48 809
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.)
Assertion
Ref Expression
pm3.48  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  \/  ch )  ->  ( ps  \/  th ) ) )

Proof of Theorem pm3.48
StepHypRef Expression
1 orc 376 . . 3  |-  ( ps 
->  ( ps  \/  th ) )
21imim2i 15 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps  \/  th ) ) )
3 olc 375 . . 3  |-  ( th 
->  ( ps  \/  th ) )
43imim2i 15 . 2  |-  ( ( ch  ->  th )  ->  ( ch  ->  ( ps  \/  th ) ) )
52, 4jaao 497 1  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  \/  ch )  ->  ( ps  \/  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359    /\ wa 360
This theorem is referenced by:  orim12d  814  tz7.48lem  6407  caubnd  11793
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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