Theorem 3orcomb 944

Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)

Assertion

Ref	Expression
3orcomb	|- ((ph \/ ps \/ ch) <-> (ph \/ ch \/ ps))

Proof of Theorem 3orcomb

Step	Hyp	Ref	Expression
1		orcom 376	. . 3 |- ((ps \/ ch) <-> (ch \/ ps))
2	1	orbi2i 505	. 2 |- ((ph \/ (ps \/ ch)) <-> (ph \/ (ch \/ ps)))
3		3orass 937	. 2 |- ((ph \/ ps \/ ch) <-> (ph \/ (ps \/ ch)))
4		3orass 937	. 2 |- ((ph \/ ch \/ ps) <-> (ph \/ (ch \/ ps)))
5	2, 3, 4	3bitr4i 268	1 |- ((ph \/ ps \/ ch) <-> (ph \/ ch \/ ps))

Syntax hints:   <-> wb 176   \/ wo 357   \/ w3o 933

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 177  df-or 359  df-3or 935

This theorem is referenced by:  eueq3  3012