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Theorem pm3.48 829
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 385 . . 3  |-  ( ps 
->  ( ps  \/  th ) )
21imim2i 14 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps  \/  th ) ) )
3 olc 384 . . 3  |-  ( th 
->  ( ps  \/  th ) )
43imim2i 14 . 2  |-  ( ( ch  ->  th )  ->  ( ch  ->  ( ps  \/  th ) ) )
52, 4jaao 509 1  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  \/  ch )  ->  ( ps  \/  th ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 368    /\ wa 369
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 370  df-an 371
This theorem is referenced by:  orim12d  834  tz7.48lem  6908  caubnd  12858
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