Theorem 3orrot 974

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 718	. 2 |- ( ( ph \/ ( ps \/ ch ) ) <-> ( ( ps \/ ch ) \/ ph ) )
2		3orass 971	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3		df-3or 969	. 2 |- ( ( ps \/ ch \/ ph ) <-> ( ( ps \/ ch ) \/ ph ) )
4	1, 2, 3	3bitr4i 211	1 |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) )

Syntax hints:   <-> wb 104   \/ wo 698   \/ w3o 967

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116  df-3or 969

This theorem is referenced by:  3mix2  1157  3mix3  1158  eueq3dc  2900  tprot  3669  sotritrieq  4303  exmidontriimlem3  7179  elnnz  9201  elznn  9207  ztri3or0  9233  zapne  9265