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Theorem pm1.5 509
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 375 . . 3  |-  ( ph  ->  ( ph  \/  ch ) )
21olcd 383 . 2  |-  ( ph  ->  ( ps  \/  ( ph  \/  ch ) ) )
3 olc 374 . . 3  |-  ( ch 
->  ( ph  \/  ch ) )
43orim2i 505 . 2  |-  ( ( ps  \/  ch )  ->  ( ps  \/  ( ph  \/  ch ) ) )
52, 4jaoi 369 1  |-  ( (
ph  \/  ( ps  \/  ch ) )  -> 
( ps  \/  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 358
This theorem is referenced by:  or12  510  meran1  25875  meran3  25877
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360
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