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Metamath Proof Explorer

Theorem pm1.5

Description: Axiom *1.5 (Assoc) of WhiteheadRussell p. 96. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm1.5 
|- ( ( ph \/ ( ps \/ ch ) ) -> ( ps \/ ( ph \/ ch ) ) )

Proof

Step Hyp Ref Expression
1 orc 
 |-  ( ph -> ( ph \/ ch ) )
2 1 olcd 
 |-  ( ph -> ( ps \/ ( ph \/ ch ) ) )
3 olc 
 |-  ( ch -> ( ph \/ ch ) )
4 3 orim2i 
 |-  ( ( ps \/ ch ) -> ( ps \/ ( ph \/ ch ) ) )
5 2 4 jaoi 
 |-  ( ( ph \/ ( ps \/ ch ) ) -> ( ps \/ ( ph \/ ch ) ) )