Theorem 3orrot 930

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 682	. 2 |- ( ( ph \/ ( ps \/ ch ) ) <-> ( ( ps \/ ch ) \/ ph ) )
2		3orass 927	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3		df-3or 925	. 2 |- ( ( ps \/ ch \/ ph ) <-> ( ( ps \/ ch ) \/ ph ) )
4	1, 2, 3	3bitr4i 210	1 |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) )

Syntax hints:   <-> wb 103   \/ wo 664   \/ w3o 923

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665

This theorem depends on definitions:  df-bi 115  df-3or 925

This theorem is referenced by:  3mix2  1113  3mix3  1114  eueq3dc  2789  tprot  3535  sotritrieq  4152  elnnz  8760  elznn  8766  ztri3or0  8792  zapne  8821