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Theorem pm3.48 734
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.) (Revised by NM, 1-Dec-2012.)
Assertion
Ref Expression
pm3.48  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  \/  ch )  ->  ( ps  \/  th ) ) )

Proof of Theorem pm3.48
StepHypRef Expression
1 orc 668 . . 3  |-  ( ps 
->  ( ps  \/  th ) )
21imim2i 12 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ps  \/  th ) ) )
3 olc 667 . . 3  |-  ( th 
->  ( ps  \/  th ) )
43imim2i 12 . 2  |-  ( ( ch  ->  th )  ->  ( ch  ->  ( ps  \/  th ) ) )
52, 4jaao 674 1  |-  ( ( ( ph  ->  ps )  /\  ( ch  ->  th ) )  ->  (
( ph  \/  ch )  ->  ( ps  \/  th ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    \/ wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  orim12d  735
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