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Theorem pm1.5 529
Description: Axiom *1.5 (Assoc) of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm1.5  |-  ( (
ph  \/  ( ps  \/  ch ) )  -> 
( ps  \/  ( ph  \/  ch ) ) )

Proof of Theorem pm1.5
StepHypRef Expression
1 orc 391 . . 3  |-  ( ph  ->  ( ph  \/  ch ) )
21olcd 399 . 2  |-  ( ph  ->  ( ps  \/  ( ph  \/  ch ) ) )
3 olc 390 . . 3  |-  ( ch 
->  ( ph  \/  ch ) )
43orim2i 525 . 2  |-  ( ( ps  \/  ch )  ->  ( ps  \/  ( ph  \/  ch ) ) )
52, 4jaoi 385 1  |-  ( (
ph  \/  ( ps  \/  ch ) )  -> 
( ps  \/  ( ph  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 374
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 190  df-or 376
This theorem is referenced by:  or12  530  meran1  31119  meran3  31121
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