Theorem 3orrot 940

Description: Rotation law for triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

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

Proof of Theorem 3orrot

Step	Hyp	Ref	Expression
1		orcom 376	. 2 |- ((ph \/ (ps \/ ch)) <-> ((ps \/ ch) \/ ph))
2		3orass 937	. 2 |- ((ph \/ ps \/ ch) <-> (ph \/ (ps \/ ch)))
3		df-3or 935	. 2 |- ((ps \/ ch \/ ph) <-> ((ps \/ ch) \/ ph))
4	1, 2, 3	3bitr4i 268	1 |- ((ph \/ ps \/ ch) <-> (ps \/ ch \/ ph))

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:  3mix2  1125  3mix3  1126  eueq3  3012  tprot  3816  nncdiv3  6278